1.

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`

Answer» 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`


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