Question

i)tan^2 theta/(sec theta - 1)^2=1 +cos theta/1-cos theta
(ii)tan A/sec A-1+tan A/sec A +1= 2 cosec A.
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Answer 1

I. LHS : =sec^2 theta -1 / (sec theta -1)^2
=(sec theta +1 ) (sec theta -1)/(sec theta -1) (sec theta -1)
=sec theta +1 / sec theta -1
=1+ cos theta/cos theta + cos theta / 1-cos theta
=1+cos theta / 1- cos theta = RHS