cosx + 2sinx = 0cosx = -2sinxcosx = -2 * sqrt(1 - cos^2 x)cos^2 x = 4(1 - cos^2 x)cos^2 x = 4 - 4cos^2 x5cos^2 x = 4cos^2 x = 4/5cosx = ±2√5 / 5
Ответ: x = arccos(±2√5 / 5) + 2πn, n ∈ Z.
cosx + 2sinx = 0
cosx = -2sinx
cosx = -2 * sqrt(1 - cos^2 x)
cos^2 x = 4(1 - cos^2 x)
cos^2 x = 4 - 4cos^2 x
5cos^2 x = 4
cos^2 x = 4/5
cosx = ±2√5 / 5
Ответ: x = arccos(±2√5 / 5) + 2πn, n ∈ Z.