Question

If ${\log }_{0.5}\sin x=1-{\log }_{0.5}\cos x$ then number of values of $x\in \left[-2\pi ,2\pi \right]$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

${\log }_{0.5}\cos x\sin x=1$

$\cos x\sin x=\frac{1}{2}$

$2\sin x\cos x=1$

$\sin 2x=1$

$2x=(2k+1)\frac{\Pi }{2}$

$No.ofvaluesofxsatisfying=4$