Question

The minimum value of $\frac{7}{4\sin x+3\cos x+2}$ is

• A. $1$
• B. $\frac{7}{9}$
• C. $\frac{7}{5}$
• D. $\frac{7}{3}$

Answer 1

The correct option is A $1$

$f\left(x\right)=\frac{7}{5\sin (x+\theta )+2}$

$f\left(x\right)$ is minimum when $\sin (x+\theta )$ is max
$f\left(x\right)=\frac{7}{5+2}$
$=1$