Question

If $y={\cos }^{-1}\left(\frac{5\cos x-12\sin x}{13}\right),x\in (0,\frac{\pi }{2}),$ then find the value of $dy/dx.$

Answer 1

$\begin{array}{c}y={\cos }^{-1}\left(\frac{5}{13}\cos x-\frac{12}{13}\sin x\right)\\ y={\cos }^{-1}\left(\cos A\cos x-\sin A\sin x\right)\\ y={\cos }^{-1}\left(\cos \left(A+x\right)\right)\\ where\cos A=\frac{5}{13}\\ y=A+x\\ \frac{dy}{dx}=1\end{array}$