SOLUTION: Show that; sin^3 theta-cos^3 theta=(sin theta-cos theta)(1+sin theta cos theta)

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Question 924143: Show that; sin^3 theta-cos^3 theta=(sin theta-cos theta)(1+sin theta cos theta)
Answer by lwsshak3(11628) About Me  (Show Source):
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Show that; sin^3 theta-cos^3 theta=(sin theta-cos theta)(1+sin theta cos theta)
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sum of cubes identity:(x^3-y^3)=(x-y)(x^2+xy+y^2)
use x for theta:
(sin^3x-cos^3x)=(sinx-cosx)(sin^2x+sinxcosx+cos^2x)=(sinx-cosx)(1+sin xcosx)