If` tan theta = tan 30^@ , tan 60^@ and। theta ` is an acute angle, then `2 theta` is equal to
यदि `tan theta = tan 30^@ , tan 60^@` और एक न्यून कोण है तो 2`theta ` का मान क्या है?

Options

A. `30^@`
B. `45^@`
C. `90^@`
D. `0^@`

Explanation

To solve the problem where \( \tan \theta = \tan 30^\circ \cdot \tan 60^\circ \) and \( \theta \) is an acute angle, we can follow these steps:

### Step 1: Calculate \( \tan 30^\circ \) and \( \tan 60^\circ \)
We know:
- \( \tan 30^\circ = \frac{1}{\sqrt{3}} \)
- \( \tan 60^\circ = \sqrt{3} \)

### Step 2: Substitute the values into the equation
Now, substitute these values into the equation:
\[ \tan \theta = \tan 30^\circ \cdot \tan 60^\circ = \left(\frac{1}{\sqrt{3}}\right) \cdot \left(\sqrt{3}\right) \]

### Step 3: Simplify the right-hand side
When we simplify the right-hand side:
\[ \tan \theta = \frac{1}{\sqrt{3}} \cdot \sqrt{3} = 1 \]

### Step 4: Determine the value of \( \theta \)
Since \( \tan \theta = 1 \), we find that:
\[ \theta = 45^\circ \]
This is because the tangent of \( 45^\circ \) is 1.

### Step 5: Calculate \( 2\theta \)
Now, we need to find \( 2\theta \):
\[ 2\theta = 2 \times 45^\circ = 90^\circ \]

### Final Answer
Thus, the value of \( 2\theta \) is \( 90^\circ \).

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