(cos^3x - sin^3x)/(cosx - sinx) = 1 + sinx cosx; Verify the Identity. I am not sure how to get to the answer. Any help getting me started would be greatly appreciated.

Question

(cos^3x - sin^3x)/(cosx - sinx) = 1 + sinx cosx; Verify the Identity.  I am not sure how to get to the answer.  Any help getting me started would be greatly appreciated.

tkhunny · Answer

You should recognize the form of the numerator.  A difference of cubes.  This can be factored.

andu1854 · Answer

Can you factor out a sincos to then create sincos(sin^2 +cos^2

anonymous · Answer

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

anonymous · Answer

As tkhunny mentioned, you have something that looks like
$$\frac{a^3-b^3}{a-b}$$
Using the difference of cubes pattern, you can factor to get
$$\frac{(a-b)(a^2+ab+b^2)}{(a-b)}$$

andu1854 · Answer

Thank  you very much... let me see what I do next, but that was very cool...

andu1854 · Answer

Thank you for the help on this one... I got it...