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Question
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
Solution
LHS = `cosec theta (1+ cos theta )( cosec theta - cot theta)`
=` (cosec theta + cosec theta xx cos theta)(cosec theta - cot theta)`
=` (cosec theta + 1/(sin theta) xx cos theta ) ( cosec theta - cot theta )`
=` ( cosec theta + cot theta )( cosec theta - cot theta)`
=` cosec^2 theta - cot^2 theta (∵ cosec^2 theta - cot^2 theta=1)`
= 1
= RHS
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