Question

The equation of the normal, to the curve y = x + sin x cos x

at x = π/2 is

• A. x = 2
• B. x = π
• C. x + π = 0
• D. 2x = π

Answer 1

Answer: (D)

2x = π

Answer 2

at x = π/2 ⇒ y = π/2 ∴ point $\left( \frac{\pi}{2},\frac{\pi}{2} \right)$

Now $\frac{dy}{dx}$ = 1 + cos²x – sin²x

$\left( \frac{dy}{dx} \right)_{\left( \frac{\pi}{2},\frac{\pi}{2} \right)}$ = 1 + 0 – 1 = 0

⇒ y – $\frac{\pi}{2}$ = $–\frac{1}{0}\left( x–\frac{\pi}{2} \right)$ ⇒ 2x = π