Maximum value of (2 sin θ+ cos θ) is?

2 sin θ + cos θ = \(\sqrt {5 }\) (\(\frac{2}{\sqrt {5 }}\)sin θ + \(\frac{1}{\sqrt {5 }}\)cos θ

multiplying and dividing by \(\sqrt {2^2 + 1^2 }\)

                                                   = \(\sqrt {5 }\) (sin θ cos ∝ + cos θ sin ∝)

                                                   = \(\sqrt {5 }\) (sin (θ + ∝))

where cos ∝ = \(\frac{2}{\sqrt {5 }}\) and sin ∝ = \(\frac{1}{\sqrt {5 }}\)

Maximum value of the expression is when sin() is maximum i.e. 1.

∴ maximum value = \(\sqrt {5 }\) × 1 = \(\sqrt {5 }\)