If $${\text{tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3 $$ the value of cosθ is?
A. 0
B. $$\frac{1}{{\sqrt 2 }}$$
C. $$\frac{1}{2}$$
D. 1
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{ tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3 \cr & \Rightarrow {\text{tan}}\left( {{{90}^ \circ } - \frac{\theta }{2}} \right) = \sqrt 3 \,\,\left[ {\pi = {{180}^ \circ }} \right] \cr & \Rightarrow \cot \frac{\theta }{2} = \sqrt 3 \cr & \Rightarrow \cot \frac{\theta }{2} = \cot {30^ \circ } \cr & \Rightarrow \frac{\theta }{2} = {30^ \circ } \cr & \Rightarrow \theta = {60^ \circ } \cr & \Rightarrow \cos {60^ \circ } = \frac{1}{2} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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