The minimum value of 3 +4 +8 is: 1. 5 2. 9 3. 7 4. 3 - Vidyadip

Question

The minimum value of $3\cos\text{x}+4\sin\text{x}+8$ is:

5
9
7
3

✓

Answer

3

Solution:

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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