Reading a pi-chart

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Reading a pi-chart

ALOK_RAJ Asked Oct 18, 2023

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Let $(x, y)$ be such that $\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2}$

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ALOK_RAJ Asked Aug 10, 2023

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Prove that $\tan \left[\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right]+\tan \left[\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right]=\frac{2 b}{a}$

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ALOK_RAJ Asked Dec 17, 2023

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Value of $\lim _{x \rightarrow \frac{\pi}{2}} \tan x \cdot \ell n \sin x$ is

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Let $f(x)=\left\{\begin{array}{ll}\frac{\sin \pi x}{5 x}, & x \neq 0 \\ k, & x=0\end{array}\right.$. If $f(x)$ is continuous at $x=0$, then $k$ is equal to

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$\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{\frac{\pi}{2}-\theta}{\cot \theta}$ is equal to

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Determine the integral values of ' $k$ ' for which the system, $\left(\tan ^{-1} x\right)^2+\left(\cos ^{-1} y\right)^2=\pi^2 k$ and $\tan ^{-1} x+\cos ^{-1} y=\frac{\pi}{2}$ possess solution and find all the solutions.

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1 Answer

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Let $g: R \rightarrow(0, \pi / 3]$ is defined by $g(x)=\cos ^{-1}\left(\frac{x^2-k}{1+x^2}\right)$. Then find the possible values of ' $k$ ' for which $g$ is surjective.

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63 views

Evaluate: $\tan \left\{2 \tan ^{-1}\left(\frac{1}{5}\right)+\frac{\pi}{4}\right\}$

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93 views

Prove that $\tan ^{-1}\left[\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right]=\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x, \frac{-1}{\sqrt{2}} \leq x \leq 1$

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by LEELADHAR YADAV

1 Answer

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LEELADHAR YADAV Asked Sep 1, 2023

53 views

If $\tan ^{-1} x+\tan ^{-1} y=\frac{\pi}{4}, x y<1$, then write the value of $x+y+x y$.

LEELADHAR YADAV Asked Sep 1, 2023

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1 Answer

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LEELADHAR YADAV Asked Sep 1, 2023

48 views

Prove that $\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)=\frac{\pi}{4}-\frac{x}{2}, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

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1 Answer

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ALOK_RAJ Asked Aug 31, 2023

123 views

If $A(2+3 \cos \alpha,-3+3 \sin \alpha), B\left(2+3 \cos \left(\alpha+\frac{2 \pi}{3}\right),-3+3 \sin \left(\alpha+\frac{2 \pi}{3}\right)\right)$

ALOK_RAJ Asked Aug 31, 2023

by ALOK_RAJ

1 Answer

0 Votes

123 Views

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Reading a pi-chart

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