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

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. sqrt((1+sinA)/(1-sinA))=secA+tanA

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (cosA)/(1+sinA)+(1+sinA)/(cosA)=2secA

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (cosectheta-cottheta)^(2)=(1-costheta)/(1+costheta)

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (sinA+cosecA)^(2)+(cosA+secA)^(2)=7+tan^(2)A+cot^(2)A

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)=tantheta

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (1+secA)/(secA)=(sin^(2)A)/(1-cosA) [Hint: Simplify LHS and RHS separately]

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+secthetacosectheta [ Hint: Write the expression in terms of sin theta and cos theta ]

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (cosecA-sinA)(secA-cosA)=1/(tanA+cotA) [ Hint: Simplify LHS and RHS separately ]

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

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (cosA-sinA+1)/(cosA+sinA-1)=cosecA+cotA , using the identity cosec^(2)A=1+cot^(2)A .