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`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
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LHS = `cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta `
=`( cot ^2 theta + (cosec theta + 1 ) ^2 ) / ((cosec theta +1) cot theta)`
=` ( cot ^2 + cosec ^2 theta + 2 cosec theta +1 )/( (cosec theta +1) cot theta)`
=`( cot ^2 theta + cosec ^2 theta +2cosec theta + cosec ^2 theta - cot^2 theta)/((cosec theta +1 ) cot theta)`
=` (2 cosec^2 theta + 2 cosec theta)/(( cosec theta +1 ) cot theta)`
=`(2 cosec theta ( cosec theta +1))/(( cosec theta +1 ) cot theta)`
=` (2 cosec theta)/(cot theta)`
=`2 xx 1/sin theta xx sin theta/ cos theta`
= 2 sec ЁЭЬГ
= RHS
Hence, LHS = RHS
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