Sin^2+2cos x sin x=0

Question

Sin^2+2cos x sin x=0

Answer 1

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