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!