verify that each x - value is a solution of the equation. tan(x) - √3 = 0 (a) x = π/3 tan(π/3) - √3 = - √3 =…

Explanation:

Step1: Recall tangent - value for $\frac{\pi}{3}$

We know that $\tan(\frac{\pi}{3})=\sqrt{3}$. Substituting $x = \frac{\pi}{3}$ into $\tan(x)-\sqrt{3}$, we get $\tan(\frac{\pi}{3})-\sqrt{3}=\sqrt{3}-\sqrt{3}$.

Step2: Recall tangent - value for $\frac{4\pi}{3}$

We know that $\tan(\frac{4\pi}{3})=\tan(\pi+\frac{\pi}{3})$. Since $\tan(A + \pi)=\tan(A)$ for any angle $A$, then $\tan(\frac{4\pi}{3})=\tan(\frac{\pi}{3})=\sqrt{3}$. Substituting $x=\frac{4\pi}{3}$ into $\tan(x)-\sqrt{3}$, we get $\tan(\frac{4\pi}{3})-\sqrt{3}=\sqrt{3}-\sqrt{3}$.

Answer:

(a) $\sqrt{3}$ (b) $\sqrt{3}$