Question

The minimum value of $3cosx+4sinx+8$ is

• A. $5$
• B. $9$
• C. $7$
• D. $3$

Answer 1

Answer: (D)

We know that,
$-\sqrt{3^2+4^2}\le 3cosx+4sinx\le \sqrt{3^2+4^2}$
$\Rightarrow -\sqrt{25}\le 3cosx+4sinx\le \sqrt{25}$
$\Rightarrow -5\le 3cosx+4sinx\le 5$
$\Rightarrow -5+8\le 3cosx+4sinx+8\le 5+8$
$\Rightarrow 3\le 3cosx+4sinx+8\le 13$
Hence, minimum value of given expression is $3$.