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?
A. $$\frac{1}{{\sqrt 2 }}$$
B. $$\sqrt 2 $$
C. $$\frac{3}{{\sqrt 2 }}$$
D. $$\frac{1}{{\sqrt 3 }}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{2cos}}\theta - \sin \theta = \frac{1}{{\sqrt 2 }} \cr & {\text{When,}} \cr & ax \mp by = m \cr & {\text{then, }}bx \mp ay = \sqrt {{a^2} + {b^2} - {m^2}} \cr & 2\cos \theta - \sin \theta = \frac{1}{{\sqrt 2 }} \cr & \Rightarrow \cos \theta + 2\sin \theta = \sqrt {4 + 1 - \frac{1}{2}} \cr & \Rightarrow \cos \theta + 2\sin \theta = \frac{3}{{\sqrt 2 }} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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