1+sin^2x=cos^2x+sinx решите уравнение

Question

1+sin^2x=cos^2x+sinx решите уравнение

Answer 1

1 + sin^2(x) = 1 - sin^2(x) + sin(x)

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

sin(x) * (2sin(x) - 1) = 0

1) sin(x) = 0

x = pi + pi*n, n ∈ Z

2) 2 sin(x) - 1 = 0; sin(x) = 1/2;

x = (-1)^n + pi/6 + pi*n, n ∈ Z