Question

How do you simplify `(sinx+cosx)^2+(sinx-cosx)^2`?

Answer 1

2

Explanation:

`(sinx+cosx)^2= sin^2x+2sinxcosx+cos^2x`
`= 1+sin2x`

`(sinx-cosx)^2= sin^2x-2sinxcosx+cos^2x`
`=1-sin2x`

`:. (sinx+cosx)^2 + (sinx-cosx)^2 = 1+sin2x + 1-sin2x = 2`