Question

2sin²x-3sinx+1=0 помогите решить!

Answer 1

$2sin^2x - 3sin x+1 = 0$

Замена: sin x = t ∈ [-1, 1]

$2t^2 - 3t + 1 = 0\\D = 9 - 4cdot 2 = 1\\x_1 = frac{3+1}{4} = 1\\x_2 = frac{2}{4} = frac{1}{2}\\\sin x = 1\\x = frac{pi}{2}+2pi n, ;nin mathbb{Z}\\\sin x = frac{1}{2}\\x = (-1)^kcdot frac{pi}{6} + pi k,;kin mathbb{Z}$