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Question: Equation of normal to the curve y = x + sin x cos x at x = \(\frac{\pi}{2}\)is...

Equation of normal to the curve y = x + sin x cos x at x = π2\frac{\pi}{2}is

A

x = p

B

x = 2

C

x + p = 0

D

x = π2\frac{\pi}{2}

Answer

x = π2\frac{\pi}{2}

Explanation

Solution

At x = π2\frac{\pi}{2} Ž y = π2\frac{\pi}{2}; (dydx)π2,π2=0\left( \frac{dy}{dx} \right)_{\frac{\pi}{2},\frac{\pi}{2}} = 0

equation is y – π2\frac{\pi}{2} = −10(x−π2)\frac{- 1}{0}\left( x - \frac{\pi}{2} \right) Ž x = π2\frac{\pi}{2}