Choose the correct answer. The minimum value of 3 +4 +8 is: - Vidyadip

MCQ

Choose the correct answer. The minimum value of $3\cos\text{x}+4\sin\text{x}+8$ is:

A
$5$
B
$9$
C
$7$
✓
$3$

✓

Answer

Correct option: D.

$3$

The given expression is $3\cos\text{x}+4\sin\text{x}+8$
Let $\text{y}=3\cos\text{x}+4\sin\text{x}+8$
$\Rightarrow\text{y}-8=3\cos\text{x}+4\sin\text{x}$
Minimum value of $\text{y}-8=-\sqrt{(3)^2+(4)^2}$
$\Rightarrow\text{y}-8=-\sqrt{9+16}=-5$
$\Rightarrow\text{y}=8-5=3$
so, the minimum value of the given expression is $3.$
Hence, the correct option is $(d).$

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