SOLUTION: How do i establish the identity
sin^3 theta - cos^3 theta/sin theta - cos theta = 1 + sin theta cos theta
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sin^3 theta - cos^3 theta/sin theta - cos theta = 1 + sin theta cos theta
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Question 876190: How do i establish the identity
sin^3 theta - cos^3 theta/sin theta - cos theta = 1 + sin theta cos theta Answer by dkppathak(439) (Show Source):
You can put this solution on YOUR website! How do i establish the identity
sin^3 theta - cos^3 theta/sin theta - cos theta = 1 + sin theta cos theta
we know a^3-b^3= (a-b)(a^2 + ab +b^2)
using formula
sin^3theta -cos^3theta = (sin theta -cos theta )(sin^2theta +cos^2 theta +sin theta. cos theta )
(sin^3 theta - cos^3 theta)/(sin theta - cos theta)
=(sin theta -cos theta )(sin^2theta +cos^2 theta +sin theta. cos theta )/sin theta - cos theta)
=(sin^2 theta + cos^2 theta + sin theta cos theta )
we know sin^2 theta + cos^2 theta =1 by substituting the value
=
=(sin^2 theta + cos^2 theta + sin theta cos theta ) = (1+ sin theta cos theta )
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