4sin2-2sin x*cosx=1

4sin2-это в квадрате

4sin^2 x - 2 sin x * cos x - sin^2 x - cos ^2 x = 0 (: cos^2 x)

4 tg^2x - 2 tg x - tg x - 1 = 0

tg x = l, x ≠ p/2 + pn, n ∈ Z

4l^2 - 3 l - 1 = 0

D = 9 + 16 = 25;

x (1,2) = 3+5/8 = 1; 3-5/8 = - 1/2;

tg x = 1;

x = p/4 + pm, m ∈ Z.

tg x = 1/2

x = arctg 1/2 + pk, k ∈ Z.