Question

The tangent and normal to the curve y = 2 sin x + sin 2x are drawn at P$\left( x = \frac{\pi}{3} \right)$, then area of the quadrilateral formed by the tangent, the normal at P and the coordinate axis is-

• A. $\frac{\pi}{3}$
• B. 3p
• C. $\frac{\pi\sqrt{3}}{2}$
• D. None of these

Answer 1

Answer: (C)

$\frac{\pi\sqrt{3}}{2}$

Answer 2

Here, $\frac{dy}{dx}$ = 0 at $\left( x = \frac{\pi}{3},y = \frac{3\sqrt{3}}{2} \right)$

Ž Tangent at x = $\frac{\pi}{3}$ is parallel to x-axis

Ž Equation of tangent is, y = $\frac{3\sqrt{3}}{2}$

Also equation of normal is, x = $\frac{\pi}{3}$

Area of quadrilateral = $\frac{\pi}{3}$ · $\frac{3\sqrt{3}}{2}$ = $\frac{\pi\sqrt{3}}{2}$sq. unit.

Hence, (3) is the correct answer.