Question

If $2{\sin }^2\theta -{\cos }^2\theta =2,$ then find the value of $\theta$ in degrees.

Answer 1

Given, $2{\sin }^2\theta -{\cos }^2\theta =2$

$\Rightarrow 2{\sin }^2\theta -1+{\sin }^2\theta =2$
$\Rightarrow 3{\sin }^2\theta -1=2$

$\Rightarrow {\sin }^2\theta =1$
$\Rightarrow \sin \theta =sin{90}^0$

$\Rightarrow \theta ={90}^{\circ }$