Question

If $\sin 2\theta =\cos 3\theta .$ The number of elements for the set $\theta$ in $0\le \theta \le 2\pi .$

• A. 2
• B. 5
• C. 6
• D. 12

Answer 1

Answer: (C)

6

Given,

$sin2\theta =cos3\theta$

$\Rightarrow cos3\theta =cos(\frac{\pi }{2}-2\theta )$

Therefore general solution is,

$3\theta =2n\pi \pm (\frac{\pi }{2}-2\theta )$, where n is any integer

$\Rightarrow \theta =2n\pi -\frac{\pi }{2},(4n+1)\frac{\pi }{10}$

thus solution in given interval is,

$\theta =\frac{\pi }{10},\frac{\pi }{2},\frac{9\pi }{10},\frac{13\pi }{10},\frac{3\pi }{2},\frac{17\pi }{10}$

Hence, option 'C' is correct.