If $${\text{0}} \leqslant \theta \leqslant {90^ \circ }$$   and $$4{\cos ^2}\theta $$   - $$4\sqrt 3 \cos \theta $$   + 3 = 0 then the value of $$\theta $$ is?

Solution (By Examveda Team)

$$\eqalign{ & 4{\cos ^2}\theta - 4\sqrt 3 \cos \theta + 3 = 0 \cr & {\text{Hit and Trial method}} \cr & {\text{Put }}\theta = {30^ \circ }{\text{option A}} \cr & 4{\cos ^2}{30^ \circ } - 4\sqrt 3 \cos {30^ \circ } + 3 = 0 \cr & \Rightarrow 4\left( {\frac{3}{4}} \right) - 4\sqrt 3 \left( {\frac{{\sqrt 3 }}{2}} \right) + 3 = 0 \cr & \Rightarrow 0 = 0 \cr} $$