Transform the equation: sin^{2} x = 1 + cos x; 1 – sin^{2} x + cos x = 0;

cos^{2} x + cos x = 0; cos x (cos x + 1) = 0

The resulting equation has two series of solutions:

if cos x = 0, then x = π/2 + 2π*n, where n is an integer (0, 1, –1, 2, –2, 3, –3, …)

if cos x = –1, then x = π + 2π*n, where n is an integer (0, 1, –1, 2, –2, 3, –3, …)

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