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Question
Prove the following identities:
`(1 + cos theta - sin^2 theta )/(sin theta (1 + cos theta)) = cot theta`
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Solution
LHS= `(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta)`
=` ((1+ cos theta )- (1-cos^2 theta))/(sin theta(1+ cos theta))`
=`(cos theta + cos^2 theta)/( sin theta ( 1+ cos theta))`
=`(cos theta ( 1+ cos theta ))/ ( sin theta ( 1+ cos theta))`
=`cos theta/ sin theta`
= cot 𝜃
= RHS
Hence, L.H.S. = R.H.S.
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