Maximum value of (2 sin θ+ cos θ) is? |
\(\sqrt {5 }\) 3 1 \(\frac{\sqrt {5 }}{2}\) |
\(\sqrt {5 }\) |
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 = \(\sqrt {5 }\) |