If tan ` 2 A = cot ( A - 60^(@))` , where 2 A is an acute angle then the value of A is

Options

A. `30^(@)`
B. `60^(@)`
C. `50^(@)`
D. `24^(@)`

Answer

To solve the equation \( \tan 2A = \cot (A - 60^\circ) \), where \( 2A \) is an acute angle, we can follow these steps:

### Step 1: Use the cotangent identity
We know that \( \cot \theta = \tan (90^\circ - \theta) \). Therefore, we can rewrite the equation as:
\[ \tan 2A = \tan (90^\circ - (A - 60^\circ)) \]
This simplifies to:
\[ \tan 2A = \tan (150^\circ - A) \]

### Step 2: Set the angles equal
Since the tangent function is periodic, we can set the angles equal to each other:
\[ 2A = 150^\circ - A \]

### Step 3: Solve for A
Now, we can solve for \( A \):
\[ 2A + A = 150^\circ \]
\[ 3A = 150^\circ \]
\[ A = \frac{150^\circ}{3} = 50^\circ \]

### Conclusion
Thus, the value of \( A \) is:
\[ A = 50^\circ \]