The number of solutions of the equation $\log _{0.5} \sin x=1-\log _{0.5} \cos x$, in $[-2 \pi, 2 \p

Question

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

Professor PC Thomas Classes · Answer

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