If $$\pi \sin \theta = 1,$$ $$\pi \cos \theta = 1{\text{,}}$$ then the value of $$\left\{ {\sqrt 3 \tan \left( {\frac{2}{3}\theta } \right) + 1} \right\}$$ is?
A. 1
B. $$\sqrt 3 $$
C. 2
D. $$\frac{1}{{\sqrt 3 }}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \pi \sin \theta = 1\,.....(i) \cr & \pi \cos \theta = 1\,.....(ii) \cr & {\text{Divide eq}}{\text{. (i) from (ii)}} \cr & \frac{{\pi \sin \theta }}{{\pi \cos \theta }} = \frac{1}{1} \cr & \tan \theta = 1 \cr & \tan \theta = \tan {45^ \circ } \cr & \theta = {45^ \circ } \cr & \therefore \sqrt 3 \tan \left( {\frac{2}{3}\theta } \right) + 1 \cr & = \sqrt 3 \tan \left( {\frac{2}{3} \times {{45}^ \circ }} \right) + 1 \cr & = \sqrt 3 {\text{ tan}}{30^ \circ } + 1 \cr & = \sqrt 3 \times \frac{1}{{\sqrt 3 }} + 1 \cr & = 2 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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