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