# Maximum value of 2sinθ + 3cosθ is?

A. 2 B. $\sqrt{13}$ C. $\sqrt{15}$ D. 1 Answer: Option B

Solution(By Apex Team)

$\begin{array}{l}(2\sin\theta+3\cos\theta)\\ \text{Maximum value of}\\ a\sin\theta+b\cos\theta\\ \begin{array}{l} =\sqrt{a^{2}+b^{2}} \\ =\sqrt{2^{2}+3^{2}} \\ =\sqrt{4+9} \\ =\sqrt{13} \end{array}\end{array}$