Question

√3(cos)^2 x - sinxcosx = 0

Answer 1

$\sqrt{3}cos^2x-sinxcosx=0\\cosx(\sqrt{3}cosx-sinx)=0\\\\\left \{ {{cosx=0} \atop {\sqrt{3}cosx-sinx=0 }} \right. \\\\cosx=0\\x=\frac{\pi }{2} + \pi k , k \in Z\\\\\sqrt{3} cosx-sinx=0\\\sqrt{3}cosx=sinx \ (:cosx)\\\sqrt{3}=tgx \\tgx=\sqrt{3}\\x=\frac{\pi }{3}+\pi k , k \in Z$

$x=\frac{\pi }{3} + \pi k , k \in Z$

$x=\frac{\pi }{2} + \pi k , k \in Z$