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Question: The equation of the normal to the curve y = x + sin x cos x at x = p/2 is –...

The equation of the normal to the curve

y = x + sin x cos x at x = p/2 is –

A

x = 2

B

x = p

C

x + p = 0

D

2x = p

Answer

2x = p

Explanation

Solution

at x = π2\frac{\pi}{2}; y = π2\frac{\pi}{2} + 0 = π2\frac{\pi}{2}

\ point = (π2,π2)\left( \frac{\pi}{2},\frac{\pi}{2} \right)

(dydx)(π2,π2)\left( \frac{dy}{dx} \right)_{\left( \frac{\pi}{2},\frac{\pi}{2} \right)} = 1 + cos2 x – sin2 x

= 1 – 1 = 0

\ normal x = x1 = π2\frac{\pi}{2}

2x=π\begin{matrix} 2x = \pi \end{matrix}