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Question
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Solution
In the given question, we need to prove `(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Using the property `sin^2 theta + cot^2 theta = 1` we get
So
`(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))`
Solving further, we get
`(cos theta + cos^2 theta)/(sin(1 + cos theta)) = (cos theta (1 + cos theta))/(sin theta(1 + cos theta))`
`= cos theta/sin theta`
`= cot theta`
Hence proved.
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