Question

The smallest positive $x$ satisfying the equation ${\log }_{\cos x}\sin x+{\log }_{\sin x}\cos x=2$ is

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

Answer 1

The correct option is C $\frac{\pi }{4}$

For ${\log }_{\cos x}\sin x+{\log }_{\sin x}\cos x=2$
$\sin x=\cos x$
This is possible for $x=\frac{\pi }{4}$