2cos²x+1 = 2√2cos(3π/2–x) Pешите pls!!!!

Question

2cos²x+1 = 2√2cos(3π/2–x) Pешите pls!!!!

Answer 1

Cos(2x) = cos^2(x) - sin^2(x) =2cos^2(x) - 1
2cos^2(x) = cos(2x) +1
____________
cos(2x) + 2  = 2√2sin(-x)
cos(2x) + 2 = - 2√2sin(x)
x = -pi/4+2pin
x = -3pi/4 = 2pin
( cos(-pi/2) +2 = -2√2sin(-pi/4) => 0+2 = -2√2*(-√2/2) =>2=2)