[tex]\displaystyle\\
\sin2x=2\cos^2x\\\\
2\sin x\cos x=2\cos^2x~~\Big|:2\cos x\\\\
\sin x=\cos x~~\Big|:\cos x\\\\
\frac{\sin x}{\cos x}=1\\\\
\text{tg }x=1\\\\
x=\text{arctg}~(1)=\frac{\pi}{4}+k\pi\\\\
\text{In intervalul:}~[0,~2\pi]~\text{tangenta este pozitiva in cadranele I si III.}\\
\text{Rezulta ca avem 2 solutii:}\\\\
\text{Solutia 1 (in cadranul I):}\\\\
\boxed{x_1=\frac{\pi}{4}=45^o}\\\\
\text{Solutia 2 (in cadranul III):}\\\\\boxed{x_2=\frac{\pi}{4}+\pi=180^o+45^o= \frac{5\pi}{4}=225^o}\\\\[/tex]
