Question

If $\theta \in (0,\frac{\pi }{2})$, the equation ${\log }_{\sin \theta }\left(\cos 2\theta \right)=2$ has

• A. no solution
• B. a unique solution
• C. two solutions
• D. infinetly many solutions

Answer 1

The correct option is B a unique solution

Solving the equation, ${\sin }^2\theta =\cos 2\theta =1-2{\sin }^2\theta$
So $\sin \theta =\pm \frac{1}{\sqrt{3}}$
but $\sin \theta >0$ for given interval.

Thus, one solution for $\sin \theta =\frac{1}{\sqrt{3}}$
Hence, option 'B' is correct.