Question

The smallest $+$ive x satisfying the equation $lo{g}_{cosx}\sin x+{\log }_{\sin x}\cos x=2$ is $\pi /4$.

Answer 1

$y+\frac{1}{y}=2$ $\Rightarrow (y-1)=0$
$\Rightarrow y=1$
$\therefore lo{g}_{\cos x}\sin x=1$ or $\sin x=\cos x$
or $\tan x=1$
$\therefore x=\pi /4$.