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

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Answer 1 · 2016-11-28T09:58:50

Please see below.

We can use here the algebraic identity

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

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

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

= $1+sinxcosx$

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