Answer :

[tex]tanx\ cosx=0;\ \ \ \ D:x\neq\frac{\pi}{2}+k\pi;\ (k\in\mathbb{Z})\\\\tanx\times cosx=0\iff tanx=0\ \vee\ cosx=0\\\\tanx=0\iff x=k\pi\\\\cosx=0\iff x=\frac{\pi}{2}+k\pi\notin D\\\\Solution:x=k\pi\ (k\in\mathbb{Z})[/tex]
AL2006
Tan = sin / cos./ / / Tan cos = (sin/cos) cos = sin = 0 / / / x = any multiple of 180 degrees.