Question

Prove that 【sin^3 thita + cos^3 thita / sin thita + cos thita】+sin thita+ cos thita= 1

Answer 1

The answer is given below :

Now, L.H.S.

$= \frac{ {sin}^{3} \alpha + {cos}^{3} \alpha }{sin \alpha + cos \alpha } + sin \alpha \: cos \alpha \\ \\ = \frac{(sin \alpha + cos \alpha )( {sin}^{2} \alpha + {cos}^{2} \alpha - sin \alpha \: cos) }{(sin \alpha + cos \alpha )} + sin \alpha \: cos \alpha \\ \\ = 1 - sin \alpha \:cos \alpha + sin \alpha \: co \alpha \\ \\ = 1$

= R.H.S. [Proved]

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