Question: If y = $\cos^{- 1}\left( \frac{5\cos x - 12\sin x}{13} \right)$, \(x \in \left( 0,\frac{\pi}{2} \r...

Question

If y = $\cos^{- 1}\left( \frac{5\cos x - 12\sin x}{13} \right)$ , $x \in \left( 0,\frac{\pi}{2} \right)$ , then $\frac{dy}{dx}$ is equal to

Answer 1

y = cos^–1 $\left( \frac{5}{13}\cos x - \frac{12}{13}\sin x \right)$

= cos^–1(cosacosx – sinasinx)

= cos^–1(cos(x + a)) = x + a

\ $\frac{dy}{dx}$ = 1

Question: If y = \(\cos^{- 1}\left( \frac{5\cos x - 12\sin x}{13} \right)\), \(x \in \left( 0,\frac{\pi}{2} \r...