cos2x+sin^2x=0,75

Interpret 0,75 as 0.75 = 3/4.

Solve cos(2x) + sin^2(x) = 3/4.

• Use cos(2x) = 1 − 2 sin^2(x). Then (1 − 2 sin^2 x) + sin^2 x = 3/4 ⇒ 1 − sin^2 x = 3/4 ⇒ sin^2 x = 1/4.

• So sin x = ±1/2.

General solutions:

• sin x = 1/2: x = π/6 + 2kπ, 5π/6 + 2kπ
• sin x = −1/2: x = 7π/6 + 2kπ, 11π/6 + 2kπ

If you want within [0, 2π): x = π/6, 5π/6, 7π/6, 11π/6 (i.e., 30°, 150°, 210°, 330°).