# Prove the following identity, where the angles involved are acute angles for which the expressions are defined.(x) ((1+tan^2A)/(1+cot^2A))=((1-tanA)/

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Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(x) ((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A

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Right hand side
=((1+tan^2A)/(1+cot^2A))
=((1+tan^2A)/((tan^2A+1)/tan^2A))
=tan^2A
Left hand side
=((1-tan^2A)/(1-cot^2A))
=((1-tan^2A)/((tan^2A-1)/tan^2A))
=tan^2A`