Cos(2x-(3п)/2)=√(2)sinx

Question

Cos(2x-(3п)/2)=√(2)sinx

Answer 1

Cos(2x-(3п)/2)=√(2)sinx
Cos((3п)/2-2x)=√(2)sinx
-sin2x-√2sinx=0
-2sinxcosx-√2sinx=0
-sinx(2cosx+√2)=0
sinx=0⇒x=πk,k∈z
2cosx+√2=0⇒cosx=-√2/2⇒x=+-3π/4+2πk,k∈z