a.MATHS,,,HELP

To prove: tan x ( 1 - sin x ) / ( 1 + cos x ) = cot x ( 1 - cos x ) / ( 1 + sin x )

L.H.S. = tan x ( 1 - sin x ) / ( 1 + cos x )

= tan x ( 1 - sin x )( 1 + sin x ) / ( 1 + cos x )( 1 + sin x )

= tan x ( 1 - sin^2 x ) / ( 1 + cos x )( 1 + sin x )

= ( tan x )( cos^2 x ) / ( 1 + cos x )( 1 + sin x )

= sin x cos x / ( 1 + cos x )( 1 + sin x )

R.H.S. = cot x ( 1 - cos x ) / ( 1 + sin x )

= cot x ( 1 + cos x )( 1 - cos x ) / ( 1 + cos x )( 1 + sin x )

= cot x ( 1 - cos ^2 x ) / ( 1 + cos x )( 1 + sin x )

= cot x sin^2 x / ( 1 + cos x )( 1 + sin x )

= sin x cos x / ( 1 + cos x )( 1 + sin x )

= L.H.S.