which value is a solution for the equation tan(x/2)=0? a. π/2 b. 2π c. 3π/2 d. π

Answer:

B. $2\pi$

Explanation:

Step1: Recall tangent - zero property

We know that $\tan\theta = 0$ when $\theta = n\pi$, where $n\in\mathbb{Z}$ (set of integers).

Step2: Set $\theta=\frac{x}{2}$

If $\tan\frac{x}{2}=0$, then $\frac{x}{2}=n\pi$.

Step3: Solve for $x$

Multiply both sides by 2: $x = 2n\pi$.

Step4: Check options

When $n = 1$, $x=2\pi$. Among the given options, only $2\pi$ satisfies the equation $\tan\frac{x}{2}=0$.