We have
`((1+tan^(2) A)/(1+ cot^(2) A))=(sec^(2) A)/("cosec"^(2)A)`
` [ because 1+ tan^(2) A= sec^(2) A " and " 1+ cot^(2) A = " cosec"^(2)A] `
` = (1)/(cos^(2) A)* sin^(2) A= (sin^(2) A)/(cos^(2) A)= tan^(2) A. `
And, `((1- tan A)/(1- cot A))^(2)= ((1-(sin A)/(cos A))^(2))/((1- (cos A)/(sin A))^(2))`
` =(((cos A - sin A)^(2))/(cos^(2)A))/(((sin A - cos A)^(2))/(sin^(2)A))= (sin^(2)A)/(cos^(2)A)= tan^(2) A.`
` therefore ((1+ tan^(2)A)/(1+ cot^(2) A))=((1- tan A)/(1- cot A))^(2) = tan ^(2) A. `
