Question

If $2{\tan }^2\theta =se{c}^2\theta$, then the general value of $\theta$ is

• A. $n\pi +\frac{\pi }{4}$
• B. $n\pi -\frac{\pi }{4}$
• C. $n\pi \pm \frac{\pi }{4}$
• D. $2n\pi \pm \frac{\pi }{4}$

Answer 1

The correct option is C

$n\pi \pm \frac{\pi }{4}$

Explanation for the correct option:

Find the value of $\theta$:

Given,

$2{\tan }^2\theta =se{c}^2\theta$

$\Rightarrow$$2\left(\frac{{\sin }^2\theta }{{\cos }^2\theta }\right)=\frac{1}{{\cos }^2\theta }$

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

$\Rightarrow$ ${\sin }^2\theta =\frac{1}{2}$

$\Rightarrow$ $\sin \theta =\pm \frac{1}{\surd 2}$

$\mathbf{\therefore }\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathit{n}\mathit{\pi }\mathbf{}\mathbf{\pm }\mathbf{}\frac{\mathbf{\pi }}{\mathbf{4}}$

Hence, Option ‘B’ is Correct.