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Question Number 16107 Answers: 0 Comments: 0

∫ ((x+2)/((x^2 +3x+3)(√(x+1)))) dx =

$$\int\:\frac{{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\right)\sqrt{{x}+\mathrm{1}}}\:{dx}\:= \\ $$

Question Number 16102 Answers: 0 Comments: 0

Question Number 16093 Answers: 0 Comments: 2

The number of solutions of ∣sin x∣ = tan x in [0, 4π] is/are?

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mid\mathrm{sin}\:{x}\mid\:=\:\mathrm{tan}\:{x}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is}/\mathrm{are}? \\ $$

Question Number 16092 Answers: 0 Comments: 5

Find the set of values of x ∈ [0, 2π] which satisfy sin x > cos x. (1) ((π/4), ((3π)/4)) ∪ (((5π)/4), 2π) (2) (0, (π/4)) ∪ (((5π)/4), 2π) (3) ((π/4), ((5π)/4)) (4) (0, ((3π)/4)) ∪ (((5π)/4), 2π)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\in\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{sin}\:{x}\:>\:\mathrm{cos}\:{x}. \\ $$$$\left(\mathrm{1}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{3}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{5}\pi}{\mathrm{4}}\right) \\ $$$$\left(\mathrm{4}\right)\:\left(\mathrm{0},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$

Question Number 16090 Answers: 1 Comments: 0

The maximum value of the expression ∣(√(sin^2 x + 2a^2 )) − (√(2a^2 − 3 − cos^2 x))∣; where ′a′ and ′x′ are real numbers, is (1) 4 (2) 2 (3) (√2) (4) 0

$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mid\sqrt{\mathrm{sin}^{\mathrm{2}} \:{x}\:+\:\mathrm{2}{a}^{\mathrm{2}} }\:−\:\sqrt{\mathrm{2}{a}^{\mathrm{2}} \:−\:\mathrm{3}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}}\mid; \\ $$$$\mathrm{where}\:'{a}'\:\mathrm{and}\:'{x}'\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers},\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\sqrt{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{0} \\ $$

Question Number 16089 Answers: 0 Comments: 2

The range of function f(θ) = sin^2 θ + (1/(1 + sin^2 θ)) is (1) [1, ∞) (2) [2, ∞) (3) [1, (3/2)] (4) [(3/2), ∞)

$$\mathrm{The}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$${f}\left(\theta\right)\:=\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\theta}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left[\mathrm{1},\:\infty\right) \\ $$$$\left(\mathrm{2}\right)\:\left[\mathrm{2},\:\infty\right) \\ $$$$\left(\mathrm{3}\right)\:\left[\mathrm{1},\:\frac{\mathrm{3}}{\mathrm{2}}\right] \\ $$$$\left(\mathrm{4}\right)\:\left[\frac{\mathrm{3}}{\mathrm{2}},\:\infty\right) \\ $$

Question Number 16088 Answers: 0 Comments: 1

∫_( 0) ^(1000) e^(x−[x]) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1000}} {\int}}{e}^{{x}−\left[{x}\right]} {dx}\:= \\ $$

Question Number 16087 Answers: 0 Comments: 1

Number of solution of equation 2[−x] + 3x = 7{x} is? (where [∙] = Greatest Integer Function & {∙} fractional function.)

$$\mathrm{Number}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{2}\left[−{x}\right]\:+\:\mathrm{3}{x}\:=\:\mathrm{7}\left\{{x}\right\}\:\mathrm{is}?\:\left(\mathrm{where}\:\left[\centerdot\right]\:=\right. \\ $$$$\mathrm{Greatest}\:\mathrm{Integer}\:\mathrm{Function}\:\&\:\left\{\centerdot\right\} \\ $$$$\left.\mathrm{fractional}\:\mathrm{function}.\right) \\ $$

Question Number 16086 Answers: 0 Comments: 1

The number of values of x which are satisfying the equation ∣x + 4∣ = 8[x] + x − 4 is? (where [∙] Greatest Integer Function)

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation}\:\mid{x}\:+\:\mathrm{4}\mid\:=\:\mathrm{8}\left[{x}\right] \\ $$$$+\:{x}\:−\:\mathrm{4}\:\mathrm{is}?\:\left(\mathrm{where}\:\left[\centerdot\right]\:\mathrm{Greatest}\:\mathrm{Integer}\right. \\ $$$$\left.\mathrm{Function}\right) \\ $$

Question Number 16085 Answers: 0 Comments: 1

Let f(sin x) + 2f(cos x) = 3 ∀ x ∈ (0, (π/2)). Then (1) f(sin x) = 1, x ∈ (0, (π/2)) (2) f(sin x) = 1, x ∈ (−1, 0) (3) f(cos x) = 1, x ∈ (0, 1) (4) f(x) = 1, x ∈ (0, 1)

$$\mathrm{Let}\:{f}\left(\mathrm{sin}\:{x}\right)\:+\:\mathrm{2}{f}\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{3}\:\forall\:{x}\:\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$$$\mathrm{Then} \\ $$$$\left(\mathrm{1}\right)\:{f}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right)\:{f}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(−\mathrm{1},\:\mathrm{0}\right) \\ $$$$\left(\mathrm{3}\right)\:{f}\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$$$\left(\mathrm{4}\right)\:{f}\left({x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$

Question Number 16082 Answers: 0 Comments: 2

Solution of equation 2[x] + 4{x} = 3x + 2 (where {∙} denotes fractional function and [∙] denotes G.I.F) is (1) {−2} (2) {−2, − (3/2)} (3) φ (4) R

$$\mathrm{Solution}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{2}\left[{x}\right]\:+\:\mathrm{4}\left\{{x}\right\}\:=\:\mathrm{3}{x} \\ $$$$+\:\mathrm{2}\:\left(\mathrm{where}\:\left\{\centerdot\right\}\:\mathrm{denotes}\:\mathrm{fractional}\right. \\ $$$$\left.\mathrm{function}\:\mathrm{and}\:\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{G}.\mathrm{I}.\mathrm{F}\right)\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left\{−\mathrm{2}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left\{−\mathrm{2},\:−\:\frac{\mathrm{3}}{\mathrm{2}}\right\} \\ $$$$\left(\mathrm{3}\right)\:\phi \\ $$$$\left(\mathrm{4}\right)\:{R} \\ $$

Question Number 16077 Answers: 0 Comments: 0

Let ABCDE be an equiangular pentagon whose side lengths are rational numbers. Prove that the pentagon is regular.

$$\mathrm{Let}\:{ABCDE}\:\mathrm{be}\:\mathrm{an}\:\mathrm{equiangular} \\ $$$$\mathrm{pentagon}\:\mathrm{whose}\:\mathrm{side}\:\mathrm{lengths}\:\mathrm{are} \\ $$$$\mathrm{rational}\:\mathrm{numbers}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{pentagon}\:\mathrm{is}\:\mathrm{regular}. \\ $$

Question Number 16081 Answers: 2 Comments: 0

A spherical balloon of 21 cm diameter is to be filled with hydrogen at NTP from a cylinder containing the gas at 20 atmosphere at 27°C. If the cylinder can hold 2.82 litres of water, calculate the number of balloons that can be filled up.

$$\mathrm{A}\:\mathrm{spherical}\:\mathrm{balloon}\:\mathrm{of}\:\mathrm{21}\:\mathrm{cm}\:\mathrm{diameter} \\ $$$$\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{filled}\:\mathrm{with}\:\mathrm{hydrogen}\:\mathrm{at}\:\mathrm{NTP} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{cylinder}\:\mathrm{containing}\:\mathrm{the}\:\mathrm{gas}\:\mathrm{at} \\ $$$$\mathrm{20}\:\mathrm{atmosphere}\:\mathrm{at}\:\mathrm{27}°\mathrm{C}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{cylinder} \\ $$$$\mathrm{can}\:\mathrm{hold}\:\mathrm{2}.\mathrm{82}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water},\:\mathrm{calculate} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{balloons}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{filled}\:\mathrm{up}. \\ $$

Question Number 16075 Answers: 0 Comments: 0

Prove that the perpendiculars dropped from the midpoints of the sides of a cyclic quadrilateral to the opposite sides are concurrent.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{perpendiculars} \\ $$$$\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quadrilateral}\:\mathrm{to}\:\mathrm{the}\:\mathrm{opposite} \\ $$$$\mathrm{sides}\:\mathrm{are}\:\mathrm{concurrent}. \\ $$

Question Number 16074 Answers: 0 Comments: 0

Let K, L, M and N be the midpoints of the sides AB, BC, CD and DA, respectively, of a cyclic quadrilateral ABCD. Prove that the orthocenters of the triangles AKN, BKL, CLM and DMN are the vertices of a parallelogram.

$$\mathrm{Let}\:{K},\:{L},\:{M}\:\mathrm{and}\:{N}\:\mathrm{be}\:\mathrm{the}\:\mathrm{midpoints}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{AB},\:{BC},\:{CD}\:\mathrm{and}\:{DA}, \\ $$$$\mathrm{respectively},\:\mathrm{of}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quadrilateral} \\ $$$${ABCD}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{orthocenters} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{triangles}\:{AKN},\:{BKL},\:{CLM}\:\mathrm{and} \\ $$$${DMN}\:\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{parallelogram}. \\ $$

Question Number 16072 Answers: 1 Comments: 3

Let ABCD be a convex quadrilateral. Prove that the orthocenters of the triangles ABC, BCD, CDA and DAB are the vertices of a quadrilateral congruent to ABCD and prove that the centroids of the same triangles are the vertices of a cyclic quadrilateral.

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{orthocenters}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangles}\:{ABC},\:{BCD},\:{CDA}\:\mathrm{and}\:{DAB} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral} \\ $$$$\mathrm{congruent}\:\mathrm{to}\:{ABCD}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{centroids}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{triangles}\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quadrilateral}. \\ $$

Question Number 16071 Answers: 1 Comments: 0

Let A′, B′ and C′ be points on the sides BC, CA and AB of the triangle ABC. Prove that the circumcircles of the triangles AB′C′, BA′C′ and CA′B′ have a common point. Prove that the property holds even if the points A′, B′ and C′ are collinear.

$$\mathrm{Let}\:{A}',\:{B}'\:\mathrm{and}\:{C}'\:\mathrm{be}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC},\:{CA}\:\mathrm{and}\:{AB}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:{ABC}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{circumcircles}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangles}\:{AB}'{C}',\:{BA}'{C}'\:\mathrm{and}\:{CA}'{B}' \\ $$$$\mathrm{have}\:\mathrm{a}\:\mathrm{common}\:\mathrm{point}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{property}\:\mathrm{holds}\:\mathrm{even}\:\mathrm{if}\:\mathrm{the}\:\mathrm{points}\:{A}', \\ $$$${B}'\:\mathrm{and}\:{C}'\:\mathrm{are}\:\mathrm{collinear}. \\ $$

Question Number 16070 Answers: 0 Comments: 0

Let ABCD be a convex quadrilateral. Prove that AB.CD + AD.BC = AC.BD if and only if ABCD is cyclic (Ptolemy′s theorem).

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral}. \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$${AB}.{CD}\:+\:{AD}.{BC}\:=\:{AC}.{BD} \\ $$$$\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{ABCD}\:\mathrm{is}\:\mathrm{cyclic}\:\left(\mathrm{Ptolemy}'\mathrm{s}\right. \\ $$$$\left.\mathrm{theorem}\right). \\ $$

Question Number 16069 Answers: 0 Comments: 0

In the interior of a quadrilateral ABCD, consider a variable point P. Prove that if the sum of distances from P to the sides is constant, then ABCD is a parallelogram.

$$\mathrm{In}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral} \\ $$$${ABCD},\:\mathrm{consider}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{point}\:{P}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{distances}\:\mathrm{from} \\ $$$${P}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{is}\:\mathrm{constant},\:\mathrm{then}\:{ABCD} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}. \\ $$

Question Number 16068 Answers: 2 Comments: 0

Let ABCD be a convex quadrilateral and let E and F be the points of intersections of the lines AB, CD and AD, BC, respectively. Prove that the midpoints of the segments AC, BD, and EF are collinear.

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{E}\:\mathrm{and}\:\mathrm{F}\:\mathrm{be}\:\mathrm{the}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{intersections}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:{AB},\:{CD}\:\mathrm{and} \\ $$$${AD},\:{BC},\:\mathrm{respectively}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{segments}\:{AC},\:{BD}, \\ $$$$\mathrm{and}\:{EF}\:\mathrm{are}\:\mathrm{collinear}. \\ $$

Question Number 16067 Answers: 1 Comments: 8

Let d, d′ be two nonparallel lines in the plane and let k > 0. Find the locus of points, the sum of whose distances to d and d′ is equal to k.

$$\mathrm{Let}\:{d},\:{d}'\:\mathrm{be}\:\mathrm{two}\:\mathrm{nonparallel}\:\mathrm{lines}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{plane}\:\mathrm{and}\:\mathrm{let}\:{k}\:>\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of} \\ $$$$\mathrm{points},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{whose}\:\mathrm{distances}\:\mathrm{to} \\ $$$${d}\:\mathrm{and}\:{d}'\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{k}. \\ $$

Question Number 16066 Answers: 2 Comments: 0

Let ABCD be a convex quadrilateral and let k > 0 be a real number. Find the locus of points M in its interior such that [MAB] + 2[MCD] = k.

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{and}\:\mathrm{let}\:{k}\:>\:\mathrm{0}\:\mathrm{be}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{points}\:{M}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\left[{MAB}\right]\:+\:\mathrm{2}\left[{MCD}\right]\:=\:{k}. \\ $$

Question Number 16065 Answers: 0 Comments: 0

Let ABCD be a convex quadrilateral. Find the locus of points M in its interior such that [MAB] = 2[MCD].

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{points}\:{M}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior} \\ $$$$\mathrm{such}\:\mathrm{that}\:\left[{MAB}\right]\:=\:\mathrm{2}\left[{MCD}\right]. \\ $$

Question Number 16064 Answers: 0 Comments: 8

Let ABCD be a convex quadrilateral and M a point in its interior such that [MAB] = [MBC] = [MCD] = [MDA]. Prove that one of the diagonals of ABCD passes through the midpoint of the other diagonal.

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{and}\:\mathrm{M}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{its}\:\mathrm{interior}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left[{MAB}\right]\:=\:\left[{MBC}\right]\:=\:\left[{MCD}\right]\:=\:\left[{MDA}\right]. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagonals}\:\mathrm{of} \\ $$$${ABCD}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{diagonal}. \\ $$

Question Number 17233 Answers: 0 Comments: 2

How to find out if cos (cos x)>sin (sin x) cos (sin x)>sin (cos x) cos (sin (cos x))>sin (cos (sin x)) cos (cos (cos x))>sin (sin (sin x)) exam questions. calculators not allowed.

$$\mathrm{How}\:\mathrm{to}\:\mathrm{find}\:\mathrm{out}\:\mathrm{if} \\ $$$$\mathrm{cos}\:\left(\mathrm{cos}\:{x}\right)>\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)>\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right)\right)>\mathrm{sin}\:\left(\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\right) \\ $$$$\mathrm{cos}\:\left(\mathrm{cos}\:\left(\mathrm{cos}\:{x}\right)\right)>\mathrm{sin}\:\left(\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\right) \\ $$$$\mathrm{exam}\:\mathrm{questions}. \\ $$$$\mathrm{calculators}\:\mathrm{not}\:\mathrm{allowed}. \\ $$

Question Number 16354 Answers: 1 Comments: 0

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