Question

The sum of all the solutions of the equation $\cos 2x+{\sin }^{2}2x=1$ which lie in the interval$[0,2\pi ]$ is equal to

• A. $4\pi$
• B. $5\pi$
• C. $7\pi$
• D. $8\pi$

Answer 1

The correct option is C $7\pi$

$\cos 2x(1-\cos 2x)=0$
$\Rightarrow \cos 2x=0,1$
$\cos 2x=0\Rightarrow 2x=\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2},\frac{7\pi }{2}$
$\cos 2x=1\Rightarrow 2x=0,2\pi ,4\pi$
Required sum $=7\pi$