Question

Prove that `(cos^3-sin^3x)/(cosx-sinx)=1+sinxcosx`?

Answer 1

Please see below.

Explanation:

We can use here the algebraic identity

`a^3-b^3=(a-b)(a^2+b^2+ab)`

Using this `(cos^3-sin^3x)/(cosx-sinx)`

= `((cosx-sinx)(cos^2x+sin^2x+sinxcosx))/(cosx-sinx)`

= `1+sinxcosx`