Question

The most general values of $\theta$, satisfying the two equations, $cos\theta =-\frac{1}{\sqrt{2}},tan\theta =1$ is

• A. $2n\pi \pm \frac{5\pi }{4}$
• B. $2n\pi +\frac{\pi }{4}$
• C. $n\pi +\frac{5\pi }{4}$
• D. $(2n+1)\pi +\frac{\pi }{4}$

Answer 1

The correct option is D $(2n+1)\pi +\frac{\pi }{4}$

$\cos \theta =-\frac{1}{\sqrt{2}}$ or $\tan \theta =1$
$\Rightarrow \theta =2n\pi \pm \frac{3\pi }{4}$ or $\theta =\frac{\pi }{4}$
$\therefore \theta =(2n+1)\pi +\frac{\pi }{4}$