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1+tan²a/1+cot²a = sec²a/csc²a = sin²a/cos²a =tan²a
(1-tana/1-cota)² ={(1-sina/ cosa)/(1-cosa/sina)}²
= {(cosa - sina)/ cosa)/(sina-cosa)/sina)}²
= [(cosa -sina)/cosa]²/[(sina-cosa)/sin a)]² = [(cos²a+sin²a - sin2a)/cos²a]/[(sin²+cos²-sin2a)/sin²]
= [(1-sin2a)/cos²a]/[(1-sin2a)/sin²a]
= [1/cos²a]/[1/sin²a]. [ cancelling (1-sin2a)]
=sin²a/cos²a = tan²a
hence proved.
(1-tana/1-cota)² ={(1-sina/ cosa)/(1-cosa/sina)}²
= {(cosa - sina)/ cosa)/(sina-cosa)/sina)}²
= [(cosa -sina)/cosa]²/[(sina-cosa)/sin a)]² = [(cos²a+sin²a - sin2a)/cos²a]/[(sin²+cos²-sin2a)/sin²]
= [(1-sin2a)/cos²a]/[(1-sin2a)/sin²a]
= [1/cos²a]/[1/sin²a]. [ cancelling (1-sin2a)]
=sin²a/cos²a = tan²a
hence proved.
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