Question

If $2\sin \theta -2i\cos \theta =1+i\sqrt{3}$ , then value of $\theta$ is

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

Answer 1

The correct option is B $\frac{5\pi }{6}$

Given, $2\sin \theta -2i\cos \theta =1+i\sqrt{3}$

Compare the real and img. part
$2\sin \theta =1;-2\cos \theta =\sqrt{3}$
$\sin \theta =\frac{1}{2}$ and $\cos \theta =-\frac{\sqrt{3}}{2}$
$\therefore \theta =\pi -\frac{\pi }{6}=\frac{5\pi }{6}$