If is a positive acute angle and 4 ^2 = 3, then the value of tan - cot /2 is?

Answer: Option B

$$\begin{array}{rl}& \text{Given 4}{\sin }^2\theta =3\\ & {\sin }^2\theta =\frac{3}{4}\\ & \sin \theta =\frac{\sqrt{3}}{2}\\ & \sin \theta =\text{sin }60^{\circ }\\ & \theta =60^{\circ }\\ & \because \tan \theta -\cot \frac{\theta }{2}\\ & =\tan 60^{\circ }-\cot \frac{{60}^{\circ }}{2}\\ & =\tan 60^{\circ }-\cot 30^{\circ }\\ & =\sqrt{3}-\sqrt{3}\\ & =0\end{array}$$