Question

Evaluate :
$\frac{1}{-{4sin}^2\theta +\frac{3}{2}sin2\theta +5}$

Answer 1

$\frac{1}{-4{\sin }^2\theta +\frac{3}{2}\sin 2\theta +5}$

$=\frac{1}{-4{\sin }^2\theta +\frac{3}{2}\times 2\sin \theta \cos \theta +5}$

$=\frac{1}{-4{\sin }^2\theta +3\sin \theta \cos \theta +5}$

$=\frac{1}{-4(1-{\cos }^2\theta )+3\sin \theta \cos \theta +5}$

$=\frac{1}{-4+4{\cos }^2\theta +3\sin \theta \cos \theta +5}$

$=\frac{1}{4{\cos }^2\theta +3\sin \theta \cos \theta +1}$