How do you prove (sinx+cosx)^4 = (1+2sinxcosx)^2?

Please refer to explanation below
Start from the left hand side
##(sinx+cosx)^4 = (1+2sinx cosx)^2##
##(sinx+cosx)(sinx+cosx)]^2##
Expand/ multiply/foil the expression
##(sin^2x + sinxcosx+sinxcosx+cos^2x)^2##
Combine like terms
##(sin^2x +cos^2x +2sinxcosx)^2##
##color(red)(sin^2x+ cos^2x= 1)##
##(1+2sinx cosx)^2## Q.E.D
Left side = right side
Prove completed!