Question

Find the solution of cos^2xsinx-3sinx=0

Answer 1

`\cos^2 x\sin x-3\sin x=0\\\\ \sin x\cdot (\cos^2 x-3)=0\\\\ \begin{array}{rcl} \sin x=0&~\text{ or }~&\cos^2 x - 3=0\\\\ \sin x=0&~\text{ or }~&\cos^2 x=3\\\\ \sin x=0&~\text{ or }~&\cos x=\pm √(3) \end{array}`


Since
`|\cos x|\le 1,` the 2nd equation has no solutions for x. So


`\sin x=0\\\\ x=k\pi~~~~\text{where }k\text{ is an integer.}`


Solution:
`S=\{x:~x=k\pi,~k\in\mathbb{Z}\}`