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