Trigonometric Functions — MATHS STD 11 Science — Question

4. 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).