If `tan(3x-15^(@))=1` then find the value of x.

Answer

To solve the equation \( \tan(3x - 15^\circ) = 1 \), we can follow these steps:

### Step 1: Understand when the tangent function equals 1
The tangent function equals 1 at specific angles. The most common angle is \( 45^\circ \). Therefore, we can set up the equation:
\[ 3x - 15^\circ = 45^\circ \]

### Step 2: Solve for \( 3x \)
Now, we add \( 15^\circ \) to both sides of the equation to isolate \( 3x \):
\[ 3x = 45^\circ + 15^\circ \]
\[ 3x = 60^\circ \]

### Step 3: Solve for \( x \)
Next, we divide both sides by 3 to find the value of \( x \):
\[ x = \frac{60^\circ}{3} \]
\[ x = 20^\circ \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{20^\circ} \]

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