Cos2x=cosx+sinx помогите плиизз

[latex]\cos2x=\cos x+\sin x\\\cos^2-\sin^2x=\cos x\sin x\\(\cos x-\sin x)(\cos x+\sin x)=\cos x+\sin x\\\cos x+\sin x=0\\\cos x=-\sin x\\tg x=-1\\x=\frac{3\pi}4+\pi n,\;n\in\mathbb{Z}\\\cos x+\sin x\neq0:\\\cos x-\sin x=0\\\cos x=\sin x\\tgx=1\\x=\frac\pi4+\pi n,\;n\in\mathbb{Z}\\OTBET:\;\frac{3\pi}4+\pi n,\;\frac{\pi}4+\pi n,\;n\in\mathbb{Z}[/latex]