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: (sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = (2)/(sin^(2)A-cos^(2)A)=(2)/(2sin^(2)A-1)=(2)/(1-2 cos^(2)A) .

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

Prove that (tan A)/(sec A-1)+(tan A)/(sec A+1)=2 cosec A .

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

( sec A + tan A ) ( 1 - sin A ) = ?

If A + B = 90^(@) , prove that sqrt((tan A tan B + tan A cot B)/(sin A sec B ) - (sin^(2) B)/(cos^(2)A)) = tan A .

Prove the following identities, 0^(@) le theta le 90^(@) . (ii) (cos A)/(1+ sin A) + (1+sin A)/(cos A) = 2 sec A