Решите уравнение sin2x+2cos^2x=0

Question

Решите уравнение
sin2x+2cos^2x=0

Answer 1

Sin2x+2cos²x=0
2sinxcosx+2cos²x=0
2cosx(sinx+cosx)=0
cosx=0                   или         sinx+cosx=0|:cosx≠0
x=π/2+πn, n∈Z                     tgx+1=0
                                              tgx=-1
                                              x=-π/4+πn, n∈Z