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Question Number 176462 Answers: 1 Comments: 1

In ΔABC given ((2a)/(tan A)) = (b/(tan B)) then ((sin^2 A−cos^2 B)/(cos^2 A+cos^2 B))=?

$${In}\:\Delta{ABC}\:{given}\:\frac{\mathrm{2}{a}}{\mathrm{tan}\:{A}}\:=\:\frac{{b}}{\mathrm{tan}\:{B}}\: \\ $$$$\:{then}\:\frac{\mathrm{sin}\:^{\mathrm{2}} {A}−\mathrm{cos}\:^{\mathrm{2}} {B}}{\mathrm{cos}\:^{\mathrm{2}} {A}+\mathrm{cos}\:^{\mathrm{2}} {B}}=? \\ $$

Question Number 176458 Answers: 5 Comments: 0

x^2 +x=1 ((x^5 +8)/(x+1))=?

$${x}^{\mathrm{2}} +{x}=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{5}} +\mathrm{8}}{{x}+\mathrm{1}}=? \\ $$

Question Number 176453 Answers: 2 Comments: 0

If , α , β , γ ∈ ( 0 , 1 ) , then prove that : (√((1−^ α ).(1−^ β ). (1−^ γ ))) +(√(α^ .β^ .γ^ )) < 1

$$ \\ $$$$\:\:\:{If}\:,\:\:\alpha\:,\:\beta\:,\:\gamma\:\in\:\left(\:\mathrm{0}\:\:,\:\:\mathrm{1}\:\right)\:\:,\:\:{then}\: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:{prove}\:\:{that}\::\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\sqrt{\left(\mathrm{1}\overset{} {−}\alpha\:\right).\left(\mathrm{1}\overset{} {−}\beta\:\right).\:\left(\mathrm{1}\overset{} {−}\gamma\:\right)}\:+\sqrt{\overset{} {\alpha}.\overset{} {\beta}.\overset{} {\gamma}}\:\:<\:\mathrm{1} \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 176449 Answers: 0 Comments: 0

A fair dice was thrown twice and it landed on a and b respectively then the probability that cubic equation x^3 −(3a+1)x^2 +(3a+2b)x−2b=0 has three distinct root

$$\mathrm{A}\:\mathrm{fair}\:\mathrm{dice}\:\mathrm{was}\:\mathrm{thrown}\:\mathrm{twice}\:\mathrm{and} \\ $$$$\mathrm{it}\:\mathrm{landed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{respectively}\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{cubic}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{3}} −\left(\mathrm{3a}+\mathrm{1}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{3a}+\mathrm{2b}\right)\mathrm{x}−\mathrm{2b}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{three}\:\mathrm{distinct}\:\mathrm{root} \\ $$$$ \\ $$

Question Number 176448 Answers: 0 Comments: 3

Suppose a^3 +b^3 +c^3 =a^2 +b^2 +c^2 =a+b+c Prove that abc=0

$$\mathrm{Suppose}\:\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} =\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} \\ $$$$=\mathrm{a}+\mathrm{b}+\mathrm{c}\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{abc}=\mathrm{0} \\ $$$$ \\ $$

Question Number 176768 Answers: 0 Comments: 0

Question Number 176440 Answers: 0 Comments: 0

Question Number 176437 Answers: 1 Comments: 0

Question Number 176427 Answers: 0 Comments: 0

Question Number 176424 Answers: 0 Comments: 0

Using perseval′s Identity Evaluate : ∫_0 ^∞ (((1−cosx)/x))^2 dx Mastermind

$$\mathrm{Using}\:\mathrm{perseval}'\mathrm{s}\:\mathrm{Identity} \\ $$$$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}}\right)^{\mathrm{2}} \mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 176423 Answers: 1 Comments: 0

Question Number 176421 Answers: 2 Comments: 0

Question Number 176399 Answers: 2 Comments: 1

a,b,c ∈R_+ ^∗ prove that a+b+c≥3^3 (√(abc))

$$\:{a},{b},{c}\:\in\mathbb{R}_{+} ^{\ast} \:\:{prove}\:{that}\:{a}+{b}+{c}\geqslant\mathrm{3}\:^{\mathrm{3}} \sqrt{{abc}} \\ $$$$ \\ $$

Question Number 176394 Answers: 0 Comments: 1

lim_(x→0) (((1−cos(√(∣x∣)))^2 )/(1−(√(cosx)))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−{cos}\sqrt{\mid{x}\mid}\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{{cosx}}}\:=\:? \\ $$

Question Number 176388 Answers: 1 Comments: 1

find lim_(x→0) ((x+sinx)/(x−sinx))

$$\:{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{sinx}}{{x}−{sinx}} \\ $$

Question Number 176387 Answers: 4 Comments: 5

x^3 +(1/x^3 ) = 1 ⇒(([x^5 +(1/x^5 )]^3 −1)/(x^5 +(1/x^5 ))) =?

$$\:\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{1}\:\Rightarrow\frac{\left[\mathrm{x}^{\mathrm{5}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }\right]^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{5}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }}\:=? \\ $$

Question Number 176384 Answers: 2 Comments: 0

Find the constant term in the expansion of the expression (2+3x)^3 ((1/x)−4)^4

$${Find}\:{the}\:{constant}\:{term}\:{in}\:{the} \\ $$$${expansion}\:{of}\:{the}\:{expression} \\ $$$$\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}}−\mathrm{4}\right)^{\mathrm{4}} \\ $$

Question Number 176393 Answers: 1 Comments: 0

show that 1+2+3+4+................ ∞ = ((−1)/8)

$${show}\:{that} \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+................\:\infty\:=\:\frac{−\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 176391 Answers: 2 Comments: 1

Question Number 176379 Answers: 1 Comments: 0

lineariser sin^5 (x)

$${lineariser}\:{sin}^{\mathrm{5}} \left({x}\right) \\ $$

Question Number 176378 Answers: 0 Comments: 0

Question Number 176375 Answers: 0 Comments: 2

lim_(x→0^+ ) ((2cos^2 ((1/x))−sin ((1/x))+3)/(x+(√x))) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{3}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:=?\: \\ $$

Question Number 176374 Answers: 1 Comments: 0

Show : (∂X/∂Y)∣_Z (∂Y/∂Z)∣_X (∂X/∂Z)∣_Y =−1

$${Show}\:: \\ $$$$\frac{\partial{X}}{\partial{Y}}\mid_{{Z}} \frac{\partial{Y}}{\partial{Z}}\mid_{{X}} \frac{\partial{X}}{\partial{Z}}\mid_{{Y}} =−\mathrm{1} \\ $$

Question Number 176371 Answers: 0 Comments: 1

Question Number 176367 Answers: 1 Comments: 1

Question Number 176360 Answers: 0 Comments: 0

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