Question

If $4{\sin }^2\theta -1=0$ and angle $\theta$ is less than ${90}^0$, find the value of $\theta$

Answer 1

$4si{n}^2\theta -1=0$
$4si{n}^2\theta =1$
$sin\theta =\frac{1}{2}$ (Neglecting the negative value, since $\theta <{90}^{\circ }$)
$sin\theta =sin{30}^{\circ }$
$\theta ={30}^{\circ }$
Let $P=co{s}^2\theta +ta{n}^2\theta$
$P=co{s}^2{30}^{\circ }+ta{n}^2{30}^{\circ }$
$=(\frac{\sqrt{3}}{2}{)}^2+(\frac{1}{\sqrt{3}}{)}^2$
$=\frac{3}{4}+\frac{1}{3}$
$=\frac{9+4}{12}$
$=\frac{13}{12}$