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Question
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
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Solution
LHS = `(1+ tan theta + cot theta )(sintheta - cos theta) `
=` sin theta + tan theta sin theta + cot theta sin theta - cos theta - tan theta cos theta - cot theta cos theta `
=`sin theta + tan theta sin theta + cos theta/sin theta xx sin theta - cos theta -sin theta/cos thetaxx cos theta - cot theta cos theta`
=`sin theta + tan theta sin theta + cos theta - cos theta - sin theta - cot theta cos theta`
=`tan theta sin theta - cot theta cos theta`
=`sin theta / cos theta xx 1/( cosec theta) - cos theta / sin theta xx 1/ sec theta`
=` 1/ (cosec theta) xx 1/ ( cosec theta ) xx sec theta - 1/ sec theta xx 1/ sec theta xx cosec theta`
=` sec theta / ( cosec^2 theta) - (cosec theta)/sec^2 theta`
= RHS
Hence, LHS = RHS
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