Question

Find all solutions in the interval [0, 2π). (sin x)(cos x) = 0

Answer 1

$\bf sin(x)cos(x)=0 \\\\[-0.35em] ~\dotfill\\\\ sin(x) = 0\implies x=sin^{-1}(0)\implies x= \begin{cases} 0\\ \pi \end{cases} \\\\[-0.35em] ~\dotfill\\\\ cos(x)=0\implies x=cos^{-1}(0)\implies x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}$