Cosx+sinx=1/2×sin2x-1 Помоги решить)

Question

Cosx+sinx=1/2×sin2x-1 Помоги решить)

Answer 1

Cosx+sinx=1/2*2sinxcosx-1
cosx+sinx=sinxcosx-1
cosx+sinx-sinxcosx-1=0
cosx(1-sinx)+(sinx-1)=0
(1-sinx)(cosx+1)=0
1) 1-sinx=0
sinx=1
x=π/2+2πn, n∈Z
2) cosx+1=0
cosx=-1
x=π+2πn,n ∈Z