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

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 (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Prove that 0 lt a lt b lt (pi)/(2), sec^(2) a lt (tan b- tan a)/(b-a) lt sec^(2) b

tan ^(2) ( sec ^(-1) 3) + cosec ^(2) ( cot ^(-1) 2) + cos ^(2) ( cos ^(-1) "" (2)/(3) + sin ^(-1) "" (2)/(3)) = __________.

Show that sqrt ((1+sin A ) /( 1-sin A))= sec A + tan A

Simplify sec A (1-sin A ) (secA+tan A)