Question

How do you verify the identity: `(sinx+cosx)^2=1+sin2x`?

Answer 1

By expanding LHS term and applying Pythagoras identity .

Explanation:

LHS=`(sinx+cosx)^2`

`LHS=sin^2x+cos^2x+2sinxcosx`

`LHS=1+sin2x` since`sin^2x+cos^2x=1 & sin2x=2sinxcosx`

`LHS=RHS`

hence proved