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} (\pi )/(2)\\\\ (3\pi )/(2) \end{cases}`