Question

TanA÷1-cotA+ cot A÷1-tanA=1+ sec A *cosec A

Answer 1

Tan a/(1-cot a) +cot a/(1-tan a)
=(sin a/,cos a) /(1-cos a/sin a) + (cos a/sin a) /(1-sin a/cos a)
=sin ^2 a/cosa(sina - cosa) +cos^2 a/sina (cosa-sina)
=sin^2a/cosa(sina-cosa) - cos^2a/sina (sina-cosa)
=(sin^3a-cos^3a)/sina.cosa(sina-cosa)
=(sina-cosa)(sin^2a+cos^2a+sinacosa)/sina.cosa(sina-cosa)
=(1+sinacosa)/sina.cosa
=(1/sinacosa)+1
=1+seca.coseca