Question

The most general value of $\theta$ which satisfy both the equations $\cos \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1$, is

• A. $2n\pi +\frac{5\pi }{4}$
• B. $2n\pi +\frac{\pi }{4}$
• C. $2n\pi +\frac{3\pi }{4}$
• D. none of these

Answer 1

The correct option is A $2n\pi +\frac{5\pi }{4}$

$\tan \theta =1\Rightarrow \theta =n\pi +\frac{\pi }{4}$ ...(1)

$\cos \theta =-\frac{1}{\sqrt{2}}=2n\pi \pm (-\frac{\pi }{4})$ ...(2)

Negative $\cos$ and positive $\tan$ is possible only in 3rd quadrant so,principle solution $=\frac{5\pi }{4}$

$\therefore \theta =2n\pi +\frac{5\pi }{4}$