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?
A. 1
B. 0
C. $$\sqrt 3 $$
D. $$\frac{1}{{\sqrt 3 }}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given 4}}{\sin ^2}\theta = 3 \cr & {\sin ^2}\theta = \frac{3}{4} \cr & \sin \theta = \frac{{\sqrt 3 }}{2} \cr & \sin \theta = {\text{sin }}{60^ \circ } \cr & \theta = {60^ \circ } \cr & \because \tan \theta - \cot \frac{\theta }{2} \cr & = \tan {60^ \circ } - \cot \frac{{{{60}^ \circ }}}{2} \cr & = \tan {60^ \circ } - \cot {30^ \circ } \cr & = \sqrt 3 - \sqrt 3 \cr & = 0 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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