Question

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

Answer 1

It is given that,
$$\begin{gathered} 2{\sin }^2\theta -{\cos }^2\theta =2 \\ \Rightarrow 2{\sin }^2\theta -2={\cos }^2\theta \\ \Rightarrow -2\left(1-{\sin }^2\theta \right)={\cos }^2\theta \\ \Rightarrow -2{\cos }^2\theta ={\cos }^2\theta \left(1-{\sin }^2\theta ={\cos }^2\theta \right) \\ \Rightarrow 3{\cos }^2\theta =0 \\ \Rightarrow \cos \theta =0 \\ \Rightarrow \theta =90° \end{gathered}$$