${\log _{{1 \over 2}}}\left| {\sin x} \right| = 2 - {\log _{{1 \over 2}}}\left| {\cos x} \right|$ $\Rightarrow$ ${\log _{{1 \over 2}}}\left| {\sin x} \right|$ + ${\log _{{1 \over 2}}}\left| {\cos x} \right|$ = 2 $\Rightarrow$ ${\log _{{1 \over 2}}}\left( {\left| {\sin x\cos x} \right|} \right)$ = 2 $\Rightarrow$ ${\left| {\sin x\cos x} \right| = {1 \over 4}}$ $\Rightarrow$ sin 2x = $\pm$ ${1 \over 2}$ $\therefore$ Number of distinct solution = 8