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Question
Prove the following identities:
`sin theta/((cot theta + "cosec" theta)) - sin theta/((cot theta - "cosec" theta)) = 2`
Theorem
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Solution
LHS = `sin theta/((cot theta + cosec theta))- sin theta/(( cot theta - cosec theta))`
= `sin theta { ((cot theta - cosec theta )-( cot theta + cosec theta ))/(( cot theta + cosec theta ) ( cot theta - cosec theta ))}`
= `sin theta { (-2 cosec theta)/(-1)} (∵ cosec^2 theta - cot^2 theta =1)`
= `sin theta . 2 cosec theta`
= `sin theta xx2xx1/ sin theta`
= 2
= RHS
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