Question

The maximum value of the expression $\frac{1}{si{n}^2\theta +3sin\theta cos\theta +5co{s}^2\theta }$ is ___

Answer 1

$f\left(\theta \right)=\frac{1}{4co{s}^2\theta +1+\frac{3}{2}sin2\theta }=\frac{1}{2cos2\theta +\frac{3}{2}sin2\theta +3}$
$\therefore$ Max.value $=\frac{1}{3-\sqrt{4+\frac{9}{4}}}=2$