Question

2cos²x + sin2x-2 = 0
Решите уравнение ​

Answer 1

2cos^2(x) + sin(2x) - 2 = 0

2cos^2(x) + 2sin(x)cos(x) - 2 = 0

2cos^2(x) + 2sin(x)cos(x) - 2sin^2(x) - 2cos^2(x) = 0

sin(x) * ( 2cos(x) - 2sin(x) ) = 0

1) sin(x) = 0 или 2) 2cos(x) = 2sin(x)

1) x = pi*n;

2) ctg(x) = 1

x = pi/4 + pi*k;