Question

show that tan^2A÷tanA-1+cot^2A÷cotA-1 =1+secA×cosecA​

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