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Prove that sin(2theta)/(1-cos2theta)=cot...

Prove that `sin(2theta)/(1-cos2theta)=cot theta`

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Prove that: a) (sin2theta)/(1+cos2theta) = tantheta b) (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cottheta

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Prove that (sin theta)/((cot theta+cosec theta))-(sin theta)/((cot theta-cosec theta))=2