Sin(x-п/4)+cos(x-п/4)=sin2x

Question

Sin(x-п/4)+cos(x-п/4)=sin2x

Answer 1

Sin(x-п/4)+cos(x-п/4)=sin2x
sinxcosπ/4-cosxsinπ/4+cosxcosπ/4+sinxsinπ/4=sin2x
√2/2*sinx-√2/2*cosx+√2/2*cosx+√2/2*sinx=sin2x
√2*sinx-2sinxcosx=0
√2sinx(1-√2cosx)=0
sinx=0⇒x=πk,k∈x
cosx=1/√2⇒x=+-π/4+2πk,k∈z