Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

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

$\sin x\cos x=0.5⟹\sin 2x=1⟹2x=n\pi +(-1{)}^n\frac{\pi }{2}$

number of solutions is $4$