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Question
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Solution
We have to prove `(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
We know that, `sin^2 theta + cos^2 theta = 1`
Multiplying both numerator and denominator by `(1 + cos theta)`, we have
`(1 - cos theta)/sin theta = ((1 - cos theta)(1 + cos theta))/(sin theta(1 + cos theta))`
`= (1 - cos^2 theta)/(sin theta(1 + cos theta))`
` = (sin^2 theta)/(sin theta(1 + cos theta))`
`= sin theta/(1 + cos theta)`
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