Question

If $\cos A=\frac{\sqrt{3}}{2}$, then $\tan 3A=?$

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. $\infty$

Answer 1

The correct option is D

$\infty$

Explanation for the correct option:

Step 1. Find the value of $\tan 3A$:

Given, $\cos A=\frac{\sqrt{3}}{2}$ …(1)

As we know,

$\cos \frac{\pi }{6}=\frac{\sqrt{3}}{2}$ …(2)

Step 2. Compare equation (1) and (2),

$A=\frac{\pi }{6}$

$\begin{array}{rcl}\therefore \tan 3A& =& \tan \frac{3\pi }{6}\\ & =& \tan \frac{\pi }{2}\\ & =& \mathbf{\infty }\end{array}$

Hence, Option ‘D’ is Correct.