Question

cos2x-sin(x+0.5π)=2​

Answer 1

Cos2x - Sin(x + 0,5π) = 2

Cos2x - Cosx = 2

2Cos²x - 1 - Cosx - 2 = 0

2Cos²x - Cosx - 3 = 0

Cosx = m , - 1 ≤ m ≤ 1

2m² - m - 3 = 0

D = (-1)² - 4 * 2 * (- 3) = 1 + 24 = 25 = 5²

$m_{1}=\frac{1-5}{4}=-1\\\\m_{2}=\frac{1+5}{4}=1,5>0-neyd\\\\Cosx=-1\\\\x=\pi+2\pi n.n\in Z\\\\Otvet:\boxed{\pi+2\pi n,n\in Z}$