Question

If $\cos 2\theta =(\sqrt{2}+1)$, then general value of $\theta$ is

• A. $2n\pi \pm \frac{\pi }{3}$
• B. $n\pi +\frac{\pi }{12}$
• C. $n\pi +\frac{7\pi }{36}$
• D. $Noneofthese$

Answer 1

The correct option is A $2n\pi \pm \frac{\pi }{3}$

$\cos 2\theta =\sqrt{2}+1$

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

$\Rightarrow -2{\sin }^2\theta =\sqrt{2}$

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

$\Rightarrow \theta =n\pi \pm \frac{\pi }{4}$