tan theta /1-cot theta + cot theta/1-tan theta = 1+ sec theta cosec theta
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explanation : let theta be "a"
LHS =tana/1-cota+cota/1-tana
=tana/1-1/tana+1/tana/1-tana
=tana/tana-1/tana+1/tana(1-tana)
=tan²a/tana-1+1/tana(1-tana)
=tan²a/tana-1 - 1/tana(tana-1)
=tan³a-1/tana(tana-1) [Lcm tana(tana-1)]
=(tana-1)(tan²a+tana+1)/tana(tana-1)
=tan²a+tana+1/tana
=tan²a/tana+tana/tana+1/tana
=tana+1+cota
=1+sina/cosa+cosa/sina
=1+sin²a+cos²a/sinacosa
=1+1/sinacosa
=1+1/cosa×1/sina
=1+secacoseca
=RHS
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