find the period. y = tan(2(x - π/6))

Explanation:

Step1: Recall period formula for tangent

The period of $y = A\tan(Bx - C)+D$ is $\frac{\pi}{|B|}$.

Step2: Identify value of B

In $y=\tan(2(x - \frac{\pi}{6}))=\tan(2x-\frac{\pi}{3})$, $B = 2$.

Step3: Calculate the period

Using the formula $\frac{\pi}{|B|}$, substitute $B = 2$. So the period is $\frac{\pi}{2}$.

Answer:

$\frac{\pi}{2}$