Question

sin2x-sin(3п/2-2x)+1=0

Answer 1

sin2x+cos2x+1=0
2sinxcosx+cos²x-sin²x+sin²x+cos²x=0
2sinxcosx+2cos²x=0
2cosx(sinx+sin(π/2-x)=0
2cosx*2sinπ/4cos(x-π/4)=0
2*2*√2/2cosxcos(x-π/4)=0
2√2cosxcos(x-π/4)=0
cosx=0⇒x=π/2+πn
cos(x-π/4)=0⇒x-π/4=π/2+πn⇒x=3π/4+πn

Answer 2

sin2x+cos2x+1=0
2sinxcosx+cos²x-sin²x+sin²x+cos²x=0