Question

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

• A. $5$
• B. $9$
• C. $7$
• D. $3$

Answer 1

Answer: (D)

We know that,
$-\sqrt{3^{2}+4^{2}}\le3\,cos\,x+4\,sin\,x\,\le \sqrt{3^{2}+4^{2}}$
$\Rightarrow -\sqrt{25} \le3\,cosx+4sinx \, \le\,\sqrt{25}$
$\Rightarrow -5 \le3cosx+4sinx \le 5$
$\Rightarrow -5+8 \le3cosx+4sinx+8 \le 5+8$
$\Rightarrow 3 \le3cosx+4sinx+8 \le 13$
Hence, minimum value of given expression is $3$.