Question

If $2si{n}^2\theta -co{s}^2\theta =2$, then find the value of $\theta$.

Answer 1

Given, $2si{n}^2\theta -co{s}^2\theta =2$

$\Rightarrow 2si{n}^2\theta -(1-si{n}^2\theta )=2$ $[\because si{n}^2\theta +co{s}^2\theta =1]$

$\Rightarrow 2si{n}^2\theta +si{n}^2\theta -1=2$

$\Rightarrow 3si{n}^2\theta =3$

$\Rightarrow si{n}^2\theta =1$ $[\because sin{90}^{\circ }=1]$

$\Rightarrow sin\theta =1=sin{90}^{\circ }$

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