Prove the following Trig Identity with reciprocals Prove that:
$$\frac{\tan x}{\sec x-1}+\frac{1-\cos x}{\sin x}=2\csc x$$
Help please! I tried so many things but couldn't get the LHS = RHS. A hint please?

HINT:
$$\frac{\tan x}{\sec x - 1}=\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2x}=\frac{1+\cos x}{\sin x}$$
