Question

If $4si{n}^2\theta -1=0$ and find angle $\theta$ and value of ${\cos }^2\theta +{\tan }^2\theta$

Answer 1

$4si{n}^2\theta -1=0$
$si{n}^2\theta =\frac{1}{4}$
$\sin \theta =\frac{1}{2}$
$sin\theta =sin30$
$\theta ={30}^{\circ }$
Now, ${\cos }^2\theta +{\tan }^2\theta$
= ${\cos }^{2}30+{\tan }^{2}30$
= $(\frac{\sqrt{3}}{2}{)}^2+(\frac{1}{\sqrt{3}}{)}^2$
= $\frac{3}{4}+\frac{1}{3}$
= $\frac{9+4}{12}$
= $\frac{13}{12}$