If 2 sin2 θ – cos2 θ = 2,
Question:

If 2 sin2 θ – cos2 θ = 2, then find the value of θ.

Solution:

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

$\Rightarrow$ $2 \sin ^{2} \theta-\left(1-\sin ^{2} \theta\right)=2$ $\left[\because \sin ^{2} \theta+\cos ^{2} \theta=1\right]$

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

$\Rightarrow$ $3 \sin ^{2} \theta=3$

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

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

$\therefore \quad \theta=90^{\circ}$