Question

Rewrite the expression sin2x+ cos2x as one involving only sinx and cosx (they can be squared, but they may not have a 2x in them).

Answer 1

sin2x+ cos2x =

sin2x = 2sinxcosx

cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2

Then:

sin2x- cos2x= 2sinxcosx+(1- 2(sinx)^2=

2sinxcosx + 1-2(sinx)^2

So:

sin2x- cos2x= 2sinxcosx+1-2(sinx)^2