Question

tanA/(1-cotA)+cotA/(1-tanA)=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

Answer 2

Answer

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$\it\huge\mathfrak\red{Hello}$]

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$<b>$]

=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

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$\it\huge\mathfrak\red{thanks}$]

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