CMAT 2017 Solved Question Paper

We know that,
-$\sqrt{{\mathit{a}}^2+{\mathit{b}}^2}$ ≤ asinx + b cosx ≤ $\sqrt{{\mathit{a}}^2+{\mathit{b}}^2}$
⇒ - $\sqrt{4^2+3^2}$ ≤ 4sinx + 3 cosx ≤ $\sqrt{4^2+3^2}$
⇒ - 5 ≤ 4 sinx + 3 cosx ≤ 5
⇒ -5 + 5 ≤ 4 sin x + 3 cos x +5 ≤ 5+5
Therefore, Maximum value of 4 sin x + 3 cos x + 5 is 10.