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Question
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Solution
We have to prove `cos^2 theta/sin theta - cosec theta + sin theta = 0`
We know that `sin^2 theta + cos^2 theta = 1`
So,
`cos^2 theta/sin theta - cosec theta + sin theta = (cos^2 theta/sin theta - cosec theta) = sin theta`
`= (cos^2 theta/sin theta - 1/sin theta) = sin theta`
`= ((cos^2 theta - 1)/sin theta) + sin theta`
`= ((-sin^2 theta )/sin theta) + sin theta`
`= - sin theta = sin theta`
= 0
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