Question

Maximum value of the expression $\sqrt{{\cos }^{2}x-10\cos x+25}+3$ is

• A. $7$
• B. $9$
• C. $3$
• D. $4$

Answer 1

The correct option is B $9$

$\sqrt{{\cos }^{2}x-10\cos x+25}+3=\sqrt{(\cos x-5{)}^2}+3=\mid (\cos x-5)\mid +3$

We know that :
$-1\le \cos x\le 1\Rightarrow -6\le \cos x-5\le -4\Rightarrow 4\le \mid (\cos x-5)\mid \le 6\Rightarrow 7\le \mid (\cos x-5)\mid +3\le 9$
Hence, the maximum value is $9.$