If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the value of $x$ is

Question

Aicharya · Accepted Answer

$\begin{aligned} & \sin ^{-1}\left(\frac{x}{13}ight)=\frac{\pi}{2}-\operatorname{cosec}^{-1}\left(\frac{13}{12}ight) \ & =\sec ^{-1}\left(\frac{13}{12}ight)=\cos ^{-1}\left(\frac{12}{13}ight) \ & 	herefore \quad \sin ^{-1}\left(\frac{x}{13}ight)=\sin ^{-1}\left(\frac{5}{13}ight) \ & 	herefore \quad x=5 \end{aligned}$

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$,…

Solution