Evaluate the following trigonometric identity to find the target value.

Given that $\cos A-\sin A=\sqrt{3}\cos A$, calculate the value of $\tan A$.

The correct answer is $1-\sqrt{3}$.

To find the value of $\tan A$, we can use the fundamental trigonometric quotient identity:

$\tan A=\frac{\sin A}{\cos A}$

We are given the linear trigonometric equation:

$\cos A-\sin A=\sqrt{3}\cos A$

Step 1: Isolate the $\sin A$ term on one side of the equation.
By subtracting $\sqrt{3}\cos A$ from both sides and adding $\sin A$ to both sides, we get:

$\cos A-\sqrt{3}\cos A=\sin A$

Step 2: Factor out the common factor $\cos A$ on the left-hand side.

$(1-\sqrt{3})\cos A=\sin A$

Step 3: Solve for $\tan A$.
Divide both sides of the equation by $\cos A$:

$1-\sqrt{3}=\frac{\sin A}{\cos A}$

Substituting $\frac{\sin A}{\cos A}=\tan A$, we arrive at the final result:

$\tan A=1-\sqrt{3}$