Sin2x+4cos^2x=0 решить уравнение

Question

Sin2x+4cos^2x=0 решить уравнение

Answer 1

Sin2x + 4cos^2x = 0
2sinxcosx + 4cos^2x = 0
cosx(2sinx + 4cosx) = 0
1)  cosx = 0
x1 = π/2 + πn, n∈Z
2) 2sinx + 4cosx = 0    /(2cosx ≠ 0)
tgx+ 2 = 0
tgx = - 2
x2 = arctg(- 2) + πk, k∈Z
x2 = - arctg(2) + πk, k∈Z