Question

The values of $\theta (0\le \theta \le \pi )$ satiesfying${\int }_0^{\theta }$ cosx dx $=\sin 2\theta$ are

• A. $0,\frac{\pi }{3}$
• B. $\frac{\pi }{4},\frac{3\pi }{4}$
• C. $\frac{\pi }{2},\pi$
• D. $\frac{\pi }{6},\frac{5\pi }{6}$

Answer 1

The correct option is A $0,\frac{\pi }{3}$

${\int }_0^{\theta }cosxdx=sin2\theta$
$sin\theta =sin2\theta$
$sin\theta =2cos\theta \cdot sin\theta$
$sin\theta =0\to \theta =0$
$cos\theta =\frac{1}{2}\to \theta =\frac{\pi }{3}$
$0,\frac{\pi }{3}$