If `tan(theta-30^(@))=(1)/(sqrt3)`, then the value of `theta` is

Options

A. `0^(@)`
B. `30^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To solve the equation \( \tan(\theta - 30^\circ) = \frac{1}{\sqrt{3}} \), we can follow these steps:

### Step 1: Identify the angle whose tangent is \( \frac{1}{\sqrt{3}} \)
The value \( \frac{1}{\sqrt{3}} \) corresponds to the angle \( 30^\circ \) because:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]

### Step 2: Set up the equation
From the equation \( \tan(\theta - 30^\circ) = \tan(30^\circ) \), we can conclude that:
\[ \theta - 30^\circ = 30^\circ + n \cdot 180^\circ \quad \text{for any integer } n \]

### Step 3: Solve for \( \theta \)
To find \( \theta \), we can rearrange the equation:
\[ \theta = 30^\circ + 30^\circ + n \cdot 180^\circ \]
\[ \theta = 60^\circ + n \cdot 180^\circ \]

### Step 4: Determine the principal value
For the principal value, we can take \( n = 0 \):
\[ \theta = 60^\circ \]

### Conclusion
Thus, the value of \( \theta \) is:
\[ \theta = 60^\circ \]