Please solve this trigonometric identity proof problem. I have completed 20; this is the hardest one. Many thanks

Question

(sin^3(x)-cos^3(x))/sin(x)-cos(x)=1+sin(x)cos(x)

Answer 1

recall that
(a^3-b^3) = (a-b)(a^2+ab+b^2)
sin^2+cos^2 = 1

and it all drops right out.