Prove that `( 1+ sec A)/( sec A) =(sin ^(2) A)/( 1-cos A) `

Prove that ((sec A -1))/( (sec A+1) ) =((1-cos A)/((1+cos A ))

Prove that (cosec A - sin A ) (sec A -cos A) = ( 1)/( tan A +cot A)

Prove that (sin A +cosec A) ^(2) +(cos A +sec A) ^(2) =7+ tan ^(2) A +cot ^(2) A

Prove that, (1+cosA+cos2A)/(sin A+sin2A)=cotA

Prove that (1+sec2A)(1+sec2^2A)(1+sec2^3A).....(1+sec2^nA)=(tan2^nA)/(tanA)

Prove that, (1+tanA)^2 + (1-tanA)^2 = 2sec^2A

Prove that , (1+sec 2 theta) (1+sec2^(2) theta)(1+ sec2^(3)theta)... ( 1+sec 2^(2) theta) = (tan 2^(n) theta)/tan theta

Prove that (tan theta+sec theta)^(2)=(1+sin theta)/(1-sin theta) .

prove that , sec ^(2) ( tan ^(-1 )2) + "cosec"^(2) ( cot ^(-1) 3) = 15 .

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1