Can you solve this; Tan 1/2X = Csc X – Cot X, using Half Angle formula?

Answer 1

tan (½ x) = √ [(1 - cos x)/(1 + cos x)] =
√[(1 - cos x)/(1 + cos x) * (1 - cos x)/(1 - cos x)] =
√[(1 - cos x)²/(1 + cos x)(1 - cos x)] =
√[(1 - cos x)²/(1 - cos² x)] =
√[(1 - cos x)²/sin² x] =
(1 - cos x)/sin x =
1/sin x - cos x/sin x =
csc x - cot x