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Question
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Solution
L.H.S. = `(costhetacottheta)/(1 + sintheta)`
= `(costhetacottheta)/(1 + sintheta) xx (1 - sintheta)/(1 - sintheta)`
= `(costhetacottheta(1 - sintheta))/(1 - sin^2theta)`
= `(costheta costheta/sintheta(1 - sintheta))/cos^2theta`
= `(1 - sintheta)/sintheta`
= `1/sintheta - 1`
= cosec θ – 1
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