If $${\text{2cos}}\theta - \sin \theta = \frac{1}{{\sqrt 2 }},$$    $$\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$   the value of $$2\sin \theta $$  + $$\cos \theta $$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{2cos}}\theta - \sin \theta = \frac{1}{{\sqrt 2 }} \cr & {\text{When,}} \cr & ax \mp by = m \cr & {\text{then, }}bx \mp ay = \sqrt {{a^2} + {b^2} - {m^2}} \cr & 2\cos \theta - \sin \theta = \frac{1}{{\sqrt 2 }} \cr & \Rightarrow \cos \theta + 2\sin \theta = \sqrt {4 + 1 - \frac{1}{2}} \cr & \Rightarrow \cos \theta + 2\sin \theta = \frac{3}{{\sqrt 2 }} \cr} $$