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Question Number 146924    Answers: 1   Comments: 0

Montrer que Ξ£_(k=0) ^(2nβˆ’1) cos^(2n) (𝛉+((k𝛑)/(2n)))= ((nC_(2n) ^n )/2^(2nβˆ’1) )

$$\boldsymbol{\mathrm{Montrer}}\:\boldsymbol{\mathrm{que}} \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\mathrm{2}\boldsymbol{{n}}βˆ’\mathrm{1}} {\sum}}\boldsymbol{{cos}}^{\mathrm{2}\boldsymbol{{n}}} \left(\boldsymbol{\theta}+\frac{\boldsymbol{{k}\pi}}{\mathrm{2}\boldsymbol{{n}}}\right)=\:\frac{\boldsymbol{{nC}}_{\mathrm{2}\boldsymbol{{n}}} ^{\boldsymbol{{n}}} }{\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}βˆ’\mathrm{1}} } \\ $$

Question Number 146923    Answers: 1   Comments: 0

if arg (((i - z)/i)) = (Ο€/4) find RemZ + ImZ = ?

$${if}\:\:\:\:{arg}\:\left(\frac{{i}\:-\:{z}}{{i}}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$$${find}\:\:\:\:{RemZ}\:+\:{ImZ}\:=\:? \\ $$

Question Number 146914    Answers: 2   Comments: 0

∣x^2 βˆ’3xβˆ’4∣ = ∣xβˆ’4∣ β‡’ x=?

$$\mid{x}^{\mathrm{2}} βˆ’\mathrm{3}{x}βˆ’\mathrm{4}\mid\:=\:\mid{x}βˆ’\mathrm{4}\mid\:\Rightarrow\:{x}=? \\ $$

Question Number 146913    Answers: 1   Comments: 0

ax=by=cz=(2/3) and ab+bc+ac=36abc find x+y+z=?

$${ax}={by}={cz}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{ab}+{bc}+{ac}=\mathrm{36}{abc} \\ $$$${find}\:\:{x}+{y}+{z}=? \\ $$

Question Number 146906    Answers: 0   Comments: 0

Question Number 147078    Answers: 0   Comments: 1

Question Number 146904    Answers: 0   Comments: 0

F = ((Gm_1 m_2 )/r^2 ) Find the value of r with the following equation.

$$\boldsymbol{\mathrm{F}}\:=\:\frac{\boldsymbol{\mathrm{Gm}}_{\mathrm{1}} \boldsymbol{\mathrm{m}}_{\mathrm{2}} }{\boldsymbol{\mathrm{r}}^{\mathrm{2}} } \\ $$$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{r}}\:\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\: \\ $$$$\boldsymbol{\mathrm{equation}}. \\ $$

Question Number 146902    Answers: 1   Comments: 0

let Ξ± and Ξ² roots of z^2 +3z+5=0 simlify U_n = Ξ£_(k=0) ^n (Ξ±^k +Ξ²^k ) and V_n =Ξ£_(k=0) ^n ((1/Ξ±^k )+(1/Ξ²^k ))

$$\mathrm{let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{roots}\:\mathrm{of}\:\:\mathrm{z}^{\mathrm{2}} +\mathrm{3z}+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{simlify}\:\mathrm{U}_{\mathrm{n}} =\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\alpha^{\mathrm{k}} \:+\beta^{\mathrm{k}} \right) \\ $$$$\mathrm{and}\:\mathrm{V}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\frac{\mathrm{1}}{\alpha^{\mathrm{k}} }+\frac{\mathrm{1}}{\beta^{\mathrm{k}} }\right) \\ $$

Question Number 146901    Answers: 1   Comments: 0

g(x)=cos(2arcsinx) calculate (dg/dx) and (d^2 g/dx^2 ) 2)find ∫_(βˆ’(1/2)) ^(1/2) g(x)dx

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{cos}\left(\mathrm{2arcsinx}\right)\:\: \\ $$$$\mathrm{calculate}\:\frac{\mathrm{dg}}{\mathrm{dx}}\:\mathrm{and}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{g}}{\mathrm{dx}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\mathrm{find}\:\int_{βˆ’\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 146899    Answers: 1   Comments: 0

f(x)=sin^5 x calculate f^((5)) ((Ο€/2))

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{\mathrm{5}} \mathrm{x}\:\:\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{5}\right)} \left(\frac{\pi}{\mathrm{2}}\right) \\ $$

Question Number 146898    Answers: 2   Comments: 0

calculate ∫_0 ^∞ ((cosx)/((x^2 +1)(x^2 +2)(x^2 +3)))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\mathrm{dx} \\ $$

Question Number 146896    Answers: 2   Comments: 0

(5/( (6)^(1/8) + 1)) βˆ™ (1/( (6)^(1/4) + 1)) βˆ™ (1/( (√6) + 1)) + 1 = ?

$$\frac{\mathrm{5}}{\:\sqrt[{\mathrm{8}}]{\mathrm{6}}\:+\:\mathrm{1}}\:\centerdot\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{6}}\:+\:\mathrm{1}}\:\centerdot\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}\:+\:\mathrm{1}}\:+\:\mathrm{1}\:=\:? \\ $$

Question Number 146895    Answers: 1   Comments: 0

(1/(2 + log_3 (25))) + (1/(2 + log_5 (9))) = ?

$$\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{3}} \left(\mathrm{25}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{5}} \left(\mathrm{9}\right)}\:=\:? \\ $$

Question Number 146886    Answers: 1   Comments: 1

Question Number 146878    Answers: 0   Comments: 0

in Ξ”ABC if sin^2 A sin B sin C+ cos Bcos C=1 then the triangle is

$${in}\:\Delta{ABC}\:{if}\:\mathrm{sin}\:^{\mathrm{2}} {A}\:\mathrm{sin}\:{B}\:\mathrm{sin}\:{C}+ \\ $$$$\mathrm{cos}\:{B}\mathrm{cos}\:{C}=\mathrm{1}\:{then}\:{the}\:{triangle}\:{is} \\ $$

Question Number 146877    Answers: 0   Comments: 0

if the sides a,b,c of a triangle ABC are in A.P. and if sin A =(sin B +sin C)cos Ξ± sin B =(sin C+sin A)cos Ξ² sin C =(sin A +sin B)cos Ξ³ then find the value of tan^2 (Ξ±/2)+tan^2 (Ξ³/2)

$${if}\:{the}\:{sides}\:{a},{b},{c}\:{of}\:{a}\:{triangle}\:{ABC} \\ $$$${are}\:{in}\:{A}.{P}.\:{and}\:{if}\: \\ $$$$\mathrm{sin}\:{A}\:=\left(\mathrm{sin}\:{B}\:+\mathrm{sin}\:{C}\right)\mathrm{cos}\:\alpha \\ $$$$\mathrm{sin}\:{B}\:=\left(\mathrm{sin}\:{C}+\mathrm{sin}\:{A}\right)\mathrm{cos}\:\beta \\ $$$$\mathrm{sin}\:{C}\:=\left(\mathrm{sin}\:{A}\:+\mathrm{sin}\:{B}\right)\mathrm{cos}\:\gamma \\ $$$${then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\mathrm{tan}\:^{\mathrm{2}} \frac{\alpha}{\mathrm{2}}+\mathrm{tan}\:^{\mathrm{2}} \frac{\gamma}{\mathrm{2}} \\ $$

Question Number 146876    Answers: 1   Comments: 0

if the maximum value of 4sin^2 x+3cos^2 x+sin (x/2)+cos (x/2)+3 is a+(√b) then find a+b

$${if}\:{the}\:{maximum}\:{value}\:{of}\: \\ $$$$\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{3cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:\frac{{x}}{\mathrm{2}}+\mathrm{cos}\:\frac{{x}}{\mathrm{2}}+\mathrm{3} \\ $$$${is}\:{a}+\sqrt{{b}}\:{then}\:{find}\:{a}+{b} \\ $$

Question Number 146875    Answers: 0   Comments: 0

In a triangle ABC, if ((sin A)/(5βˆ’x))=((sin B)/(3xβˆ’1))=((sin C)/(2x+5)) then find integral solutions x?

$${In}\:{a}\:{triangle}\:{ABC},\:{if}\: \\ $$$$\frac{\mathrm{sin}\:{A}}{\mathrm{5}βˆ’{x}}=\frac{\mathrm{sin}\:{B}}{\mathrm{3}{x}βˆ’\mathrm{1}}=\frac{\mathrm{sin}\:{C}}{\mathrm{2}{x}+\mathrm{5}}\:{then}\:{find} \\ $$$$\:{integral}\:{solutions}\:{x}? \\ $$

Question Number 146874    Answers: 0   Comments: 0

let the line joining through orthocenter and circumcenter of a triangle ABC is parallel to the base BC then find tan B.tan C

$${let}\:{the}\:{line}\:{joining}\:{through}\: \\ $$$${orthocenter}\:{and}\:{circumcenter}\: \\ $$$${of}\:{a}\:{triangle}\:{ABC}\:{is}\:{parallel}\:{to}\: \\ $$$${the}\:{base}\:{BC}\:{then}\:{find}\:\:\mathrm{tan}\:{B}.\mathrm{tan}\:{C} \\ $$

Question Number 146865    Answers: 1   Comments: 0

arcsin(x^2 βˆ’4) = arcsin(2x + 4) β‡’ x = ?

$${arcsin}\left({x}^{\mathrm{2}} βˆ’\mathrm{4}\right)\:=\:{arcsin}\left(\mathrm{2}{x}\:+\:\mathrm{4}\right) \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$

Question Number 146866    Answers: 1   Comments: 0

((sin^6 𝛂 + cos^6 𝛂 - 1)/(sin^4 𝛂 - sin^2 𝛂)) = ?

$$\frac{{sin}^{\mathrm{6}} \boldsymbol{\alpha}\:+\:{cos}^{\mathrm{6}} \boldsymbol{\alpha}\:-\:\mathrm{1}}{{sin}^{\mathrm{4}} \boldsymbol{\alpha}\:-\:{sin}^{\mathrm{2}} \boldsymbol{\alpha}}\:=\:? \\ $$

Question Number 146863    Answers: 1   Comments: 1

Question Number 146910    Answers: 1   Comments: 0

Question Number 146911    Answers: 0   Comments: 0

(dy/dx) = ((2cos^2 xβˆ’sin^2 x+y^2 )/(2cos x)) y(0)=βˆ’1 & y(1)=sin x

$$\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}βˆ’\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{y}^{\mathrm{2}} }{\mathrm{2cos}\:\mathrm{x}} \\ $$$$\:\:\:\mathrm{y}\left(\mathrm{0}\right)=βˆ’\mathrm{1}\:\&\:\mathrm{y}\left(\mathrm{1}\right)=\mathrm{sin}\:\mathrm{x}\: \\ $$

Question Number 147008    Answers: 0   Comments: 1

find the number of values of cot ΞΈ where θ∈[(Ο€/(12)) (Ο€/2)] satisfying the equation [tan ΞΈ.[cot ΞΈ]]=1 ? (where [x] is greatest integer less than or equal to x)

$${find}\:{the}\:{number}\:{of}\:{values}\:{of}\:\mathrm{cot}\:\theta\: \\ $$$${where}\:\theta\in\left[\frac{\pi}{\mathrm{12}}\:\frac{\pi}{\mathrm{2}}\right]\:{satisfying}\:{the}\: \\ $$$${equation}\:\left[\mathrm{tan}\:\theta.\left[\mathrm{cot}\:\theta\right]\right]=\mathrm{1}\:?\: \\ $$$$\left({where}\:\left[{x}\right]\:{is}\:{greatest}\:{integer}\right. \\ $$$$\left.{less}\:{than}\:{or}\:{equal}\:{to}\:{x}\right) \\ $$

Question Number 147007    Answers: 1   Comments: 0

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