Решите уравнение 2sin2 х-sinx cosx-cos2x=0

2sin2 х - sinx cosx - cos2x = 0

4sinx cosx - sinx cosx - cos2x = 0

3sinx cosx - (cos^2x - sin^2x) = 0

sin^2x + 3 sinx cosx - cos^2x = 0 / / : cos^2x ≠ 0

tg^2x + 3tgx - 1 = 0

D = 9 + 4 = 13

tgx = (- 3 + √13) / 2 = = > x = arctg ((- 3 + √13) / 2) + pik, k ∈ Z

tgx = (- 3 - √13) / 2 = = > x = arctg ((- 3 - √13) / 2) + pik, k ∈ Z

Ответ:

x = arctg ((- 3 + √13) / 2) + pik, k ∈ Z

x = arctg ((- 3 - √13) / 2) + pik, k ∈ Z