Question

решите плиз
2cos^2(x-п/8)-2sin^2(x-п/8)=2​

Answer 1

$2cos^2(x-\frac{\pi}{8})-2sin^2(x-\frac{\pi}{8})=2\, |:2\\\\cos^2(x-\frac{\pi}{8})-sin^2(x-\frac{\pi}{8})=1\\\\cos(2x-\frac{\pi}{4} )=1\\\\2x-\frac{\pi}{4}=\frac{\pi}{2}+2\pi n\; ,\; n\in Z\\\\2x=\frac{3\pi }{4}+2\pi n\; ,\; n\in Z\\\\x=\frac{3\pi }{8}+\pi n\; ,\; n\in Z$