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

• A. 1
• B. – 1
• C. 0
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

Let $\cos\alpha = \frac{5}{13}$. Then $\sin\alpha = \frac{12}{13}$.

So, $y = \cos^{- 1}\{\cos\alpha.\cos x - \sin\alpha.\sin x\}$

$\therefore y = \cos^{- 1}\{\cos(x + \alpha)\} = x + \alpha$

($\because x + \alpha$ is in the first or the second quadrant)

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