If $${\text{tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3 $$     the value of cosθ is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{ tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3 \cr & \Rightarrow {\text{tan}}\left( {{{90}^ \circ } - \frac{\theta }{2}} \right) = \sqrt 3 \,\,\left[ {\pi = {{180}^ \circ }} \right] \cr & \Rightarrow \cot \frac{\theta }{2} = \sqrt 3 \cr & \Rightarrow \cot \frac{\theta }{2} = \cot {30^ \circ } \cr & \Rightarrow \frac{\theta }{2} = {30^ \circ } \cr & \Rightarrow \theta = {60^ \circ } \cr & \Rightarrow \cos {60^ \circ } = \frac{1}{2} \cr} $$