Giải phương trình: cos^2 x - sin2x = 0

PT \( \Leftrightarrow {\cos ^2}x - 2\sin x\cos x = 0 \Leftrightarrow \cos x\left( {\cos x - 2\sin x} \right) = 0\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{\cos x = 0}\\{\cos x = 2\sin x}\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{\cos x = 0}\\{\tan x = \frac{1}{2}}\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{2} + k\pi }\\{x = \arctan \frac{1}{2} + k\pi }\end{array}} \right.\left( {k \in \mathbb{Z}} \right)\) .