If 2cos - = 1 2 , ( 0^ < < 90^ ) the value of 2 + is?

Answer: Option C

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