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

1 Answer
Nov 30, 2015

Please refer to explanation below

Explanation:

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!