Prove that \[ \frac{\sin 2x}{1-\cos 2x}=\cot x \]
Proof:
\[
LHS=\frac{\sin 2x}{1-\cos 2x}
\]
Using the identities:
\[
\sin 2x=2\sin x\cos x
\]
\[
1-\cos 2x=2\sin^2 x
\]
Substituting these values:
\[
LHS=\frac{2\sin x\cos x}{2\sin^2 x}
\]
\[
=\frac{\sin x\cos x}{\sin^2 x}
\]
\[
=\frac{\cos x}{\sin x}
\]
\[
=\cot x
\]
Hence proved,
\[
\boxed{\frac{\sin 2x}{1-\cos 2x}=\cot x}
\]