Verify the following identity?

Question

cscx - (tanx/2) = cotx

Answer 1

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

Answer 2

tan x/2 = (sin x/2 )/ (cos x/2)

= 2 sin x/2 cos x/2/( 2 cos^2 x/2)

= sin x/( 1+ cos x)

as sin x = 2 sin x/2 cos x/2

and cos x = 2 cos^2 x/2 - 1

so

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

= cosec x - cot x

or cosec x - tan x/2 = cot x