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`

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

((1+tan^(2)A)/(1+cot^(2)A))=((1-tan A)/(1-cot A))^(2)=tan^(2)A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(vi) sqrt((1+sin A)/(1-sin A))=sec A+tan A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(iv) (1+sec A)/(sec A)=(sin^(2)A)/(1-cos A)

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(i) (csc theta-cot theta)^(2)=(1-cos theta)/(1+cos theta)

Prove the following identity,where the angles invorved are acute angles for which the expressions are defined.(ii) (cos A)/(1+sin A)+(1+sin A)/(cos A)=2sec A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.( ix) (csc A-sin A)(sec A-cos A)=(1)/(tan A+cot A)[ Hint : Simplify L.HS and RHS separately]

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(iii) (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta cos ec theta

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(cos A-sin A+1)/(cos A+sin A-1)=cos ecA+cot A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(viii) (sin A+cos ecA)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A