The value of `(Sin 2A)/(1 - cos 2 A)`is

Options

A. `cosec A`
B. `tan A`
C. `cot A`
D. `tan 2A`

Answer

To solve the expression \(\frac{\sin 2A}{1 - \cos 2A}\), we can use trigonometric identities.

### Step-by-step Solution:

1. **Use the double angle identities**:
We know that:
\[ \sin 2A = 2 \sin A \cos A \]
and
\[ \cos 2A = 1 - 2 \sin^2 A \]
or
\[ \cos 2A = 2 \cos^2 A - 1 \]

2. **Substituting \(\cos 2A\)**:
We can rewrite \(1 - \cos 2A\) using the identity for \(\cos 2A\):
\[ 1 - \cos 2A = 1 - (1 - 2 \sin^2 A) = 2 \sin^2 A \]

3. **Substituting into the original expression**:
Now substitute \(\sin 2A\) and \(1 - \cos 2A\) into the expression:
\[ \frac{\sin 2A}{1 - \cos 2A} = \frac{2 \sin A \cos A}{2 \sin^2 A} \]

4. **Simplifying the expression**:
We can simplify the fraction:
\[ = \frac{2 \sin A \cos A}{2 \sin^2 A} = \frac{\cos A}{\sin A} = \cot A \]

Thus, the value of \(\frac{\sin 2A}{1 - \cos 2A}\) is \(\cot A\).

### Final Answer:
\[ \frac{\sin 2A}{1 - \cos 2A} = \cot A \]