Question

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

Answer 1

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!