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Question: If y = sin<sup>–1</sup>(cosx), x∈\(\left( 0,\frac{\pi}{2} \right)\) then \(\frac{dy}{dx}\)is –...

If y = sin–1(cosx), x∈(0,π2)\left( 0,\frac{\pi}{2} \right) then dydx\frac{dy}{dx}is –

A

–1

B

sin x

C

sin2x

D

None of these

Answer

–1

Explanation

Solution

dydx\frac{dy}{dx} = 11−cos⁡2x\frac{1}{\sqrt{1 - \cos^{2}x}}× –sin x = –sin⁡x∣sin⁡x∣\frac{–\sin x}{|\sin x|}

if x < π2\frac{\pi}{2}|sinx| = sin x

⇒ dydx\frac{dy}{dx}= –sin⁡xsin⁡x\frac{–\sin x}{\sin x}= – 1