If sin ^{-1}left(frac{3}{5}right)+cos ^{-1}le | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\sin ^{-1}\left(\frac{3}{5}\right) = x$ and $\cos ^{-1}\left(\frac{12}{13}\right) = y$. Then $\sin x = \frac{3}{5} \implies \cos x = \sqrt{1

Vedclass · Accepted Answer

$\frac{56}{65}$

Vedclass · Answer

(A) Let $\sin ^{-1}\left(\frac{3}{5}ight) = x$ and $\cos ^{-1}\left(\frac{12}{13}ight) = y$. Then $\sin x = \frac{3}{5} \implies \cos x = \sqrt{1 - (\frac{3}{5})^2} = \frac{4}{5}$. And $\cos y = \frac{12}{13} \implies \sin y = \sqrt{1 - (\frac{12}{13})^2} = \frac{5}{13}$. We are given $x + y = \sin ^{-1} \alpha$,which means $\sin(x + y) = \alpha$. Using the identity $\sin(x + y) = \sin x \cos y + \cos x \sin y$: $\alpha = (\frac{3}{5}) 	imes (\frac{12}{13}) + (\frac{4}{5}) 	imes (\frac{5}{13})$ $\alpha = \frac{36}{65} + \frac{20}{65} = \frac{56}{65}$.

If $\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$,then $\alpha=$

Similar Questions

$\tan ^{-1} 2+\tan ^{-1} 3=$

The value of $\tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)$ is

If $\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1} \left(\frac{2^{p-1}}{1+2^{2p-1}}\right) = \tan^{-1} \alpha$, then $\tan \alpha$ is equal to . . . . . . .

If $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{3}$ and $\cot ^{-1}\left(\frac{1}{x}\right)-\cot ^{-1}\left(\frac{1}{y}\right)=0$,then $2 x^2+y^2-x y=$

If $y = \sin^{-1} \left( \frac{5x + 12\sqrt{1-x^2}}{13} \right)$,then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module