Question

Prove That - {(cos^3A+sin^3A)/(cosA+sinA)} +{ (cos^3A-sin^3A)/(cosA-sinA)} = 2

Answer 1

\[\frac{\cos^3A+\sin^3A}{\cos A+\sin A}+\frac{\cos^3A-\sin^3A}{\cos A-\sin A}=2\]
Factor both numerators:
\[a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)\]