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Question
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
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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