Is this correct?

Question

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

LS = RS

Answer 1

that is correct, but it would have been simpler when you got the LS expanded, to see that you had

LS = sin^2x - 2sinxcosx + cos^2x
= sin^2x + cos^2x -2sinxcosx
= 1 - 2sinxcosx