Question

4sin2-2sin x*cosx=1 4sin2-это в квадрате

Answer 1

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.