Question

VERIFY (SIN^3X+COS^3X)/(SINX+COSX)=1-SINXCOSX

Answer 1

Factor the numerator on the left:
\[\sin^3x+\cos^3x=(\sin x+\cos x)(\sin^2x-\sin x\cos x+\cos^2x)\]

Answer 2

okay.. what do I do after?

Answer 3

\[\text{left}=\frac{(\sin x+\cos x)(\sin^2x-\sin x\cos x+\cos^2x)}{\sin x+\cos x}=\sin^2x-\sin x\cos x+\cos^2x\]