Question

Помогите решить уравнение 3sin^2x+sin2x+cos^2x=1

Answer 1

$3sin^{2} x+sin2x+cos^{2} x=1 \ 3sin^{2} x+2sinxcosx+cos^{2} x-1=0 \ 3sin^{2} x+2sinxcosx+cos^{2} x-sin^{2} x-cos^{2} x=0 \ 3sin^{2} x+2sinxcosx-sin^{2} x=0 \ 2sin^{2} x+2sinxcosx=0 \ 2(sin^{2} x+sinxcosx)=0/:2 \ sin^{2} x+sinxcosx=0 \ sinx(sinx+cosx)=0 \ sinx=0 \ x= pi n$

$sinx+cosx=0/:cosx \ cosx neq 0 \ x neq frac{ pi }{2}+ pi a \ tgx+1=0 \ tgx=-1 \ x=- frac{ pi }{4} + pi m$

n ∈  Z
m ∈  Z
a   ∈ Z