Question

Prove the identity: (cos^3x+sin^3x)/(cos^4x-sin^4x)=(1-cosxsinx)/(cosx-sinx)

Answer 1

If anyone could just work this out for me I could find the identities to prove it on my own!

Answer 2

I just don't know where to start with this problem..

Answer 3

\[\frac{\cos^3x+\sin^3x}{\cos^4x-\sin^4x}=\frac{(\cos x+\sin x)\left(\cos^2x-\cos x\sin x+\sin^2x\right)}{(\cos x-\sin x)(\cos x+\sin x)\left(\cos^2x+\sin^2x\right)}\]

Answer 4

This result due to the sum/difference of cubes/squares formulas,
\[a^3\pm b^3=(a\pm b)(a^2\pm ab+b^2)\\
a^2-b^2=(a-b)(a+b)\]