Sin^2+2cos x sin x=0

Решение

Sin^2x+2cos x sin x=0

sinx (sinx + 2cosx) = 0

1) sinx = 0

x = πk, k ∈ Z

2) sinx + 2cosx = 0 делим на cosx ≠ 0

tgx + 2 = 0

tgx = - 2

x = arctg (-2) + πn, n ∈ Z

x = - arctg2 + πn, n ∈Z