tan A /1-tan A + cot A/1-cot A = K+ tan A+ cot A. find K
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L.H.S =tanA1−cotA+cotA1−tanA
=tanA1−1tanA+1tanA1−tanA
=tan2AtanA−1−1tanAtanA−1
=1tanA−1tan3A–1tanA
=1tanA−1(tanA−1)tan2A+tanA+1tanA
=tan2A+tanA+1tanA
=tanA+1+1tanA
=tanA+1+cotA
= R. H. S
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