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

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

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

Prove that (cos C + cos A)/(c + a) + (cos B)/(b) = (1)/(b)

Prove that, (sec 8 alpha -1)/(sec 4 alpha-1)= (tan 8 alpha)/(tan 2 alpha

Prove that ""(1)/(2)cos^(-1)""((5cos x+3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan""(x)/(2))

prove that , tan(2tan ^(-1) sqrt((1+cos theta )/(1- cos theta )))+tan theta =0

prove that , sin ^(-1) cos sin ^(-1 )x+cos ^(-1) sin cos ^(-1) ""x=(pi)/(2)

Prove that, sin^(2)A cos^(4) A = 1/16 + 1/32 cos2A - 1/16 cos 4 A - 1/32 cos 6 A

Prove that sqrt((1+costheta)/(1-costheta))+sqrt((1-cos theta)/(1+cos theta))=2 " cosec"theta.

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