Question

Решите уравнение cos^2x+cosx=sin^2x

Answer 1

$cos^{2}x+cosx=sin^{2}x\\cos^{2}x-sin^{2}x+cosx=0\\cos^{2}x-(1-cos^{2}x)+cosx=0\\2cos^{2}x+cos^{2}x-1=0\\cosx=u\\2u^{2}+u-1=0\\D:1+8=9\\x_1,_2= \frac{-1\pm 3}{4} \\x_1= \frac{1}{2} \\x_2=-1\\\\1)cosx = \frac{1}{2}\\x=\pm arccos \frac{1}{2} +2\pi n\\x=\pm \frac{\pi}{3} +2\pi n, n\in Z\\\\2)cosx=-1\\x=\pi+2\pi n,n\in Z.$