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!