Sin x - корень из 3* cosx=1

[latex]\sin{x}-\sqrt{3}\cos{x}=1[/latex] Делим на 2 [latex]\frac{1}{2}\sin{x}-\frac{\sqrt{3}}{2}\cos{x}=\frac{1}{2}[/latex] [latex]\cos{\frac{\pi}{3}}\sin{x}-\sin{\frac{\pi}{3}}\cos{x}=\frac{1}{2}[/latex] [latex]\sin{(x-\frac{\pi}{3})}=\frac{1}{2}[/latex] [latex]x-\frac{\pi}{3}=\frac{\pi}{4}+\pi\cdot{k}, k\in{\mathbb{Z}}[/latex] [latex]x=\frac{7\pi}{12}+\pi{k},k\in{\mathbb{Z}}[/latex]