If $$\theta $$ is a positive acute angle and $${\text{4}}{\sin ^2}\theta $$   = 3, then the value of $${\text{tan}}\theta $$  - $$cot\frac{\theta }{2}$$  is?

Solution (By Examveda Team)

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