Question

For the curve $y=3\sin \theta \cos \theta ,x=e^{\theta }\sin \theta ,0\le \theta \le \pi$; the tangent is parallel to $x$ -axis when $\theta$ is

• A. $0$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is C $\frac{\pi }{4}$

$\frac{dy}{dx}=0$

$\frac{dy}{d\theta }=d\frac{3}{2}\left(sin2\theta \right)$

$\frac{dy}{d\theta }=d\frac{3}{4}\left(cos2\theta \right)$ ---- (1)

$\frac{dy}{d\theta }=e^{\theta }sin\theta +e^{\theta }cos\theta$ ---- (2)

$\frac{dx}{dy}=\frac{3}{4}\frac{cos2\theta }{e^{\theta }(sin\theta +cos\theta )}=0$

$cos2\theta =0$

$2\theta =\pi /2$

$\theta =\pi /4$