Question

The general value of θ in the equation $\cos \theta =\frac{1}{\sqrt{2}},\tan \theta =-1$ is

• A. $2n\pi \pm \frac{\pi }{6},n\in I$
• B. $2n\pi \pm \frac{7\pi }{4},n\in I$
• C. $n\pi +(-1{)}^n.\frac{\pi }{3},n\in I$
• D. $n\pi +(-1{)}^n.\frac{\pi }{4},n\in I$

Answer 1

The correct option is B $2n\pi \pm \frac{7\pi }{4},n\in I$

Here $\theta$ lies in the $4^{th}$ quadrant.
$\therefore \theta =2\pi -\frac{\pi }{4}=\frac{7\pi }{4}$
Now considering the equation,
$\cos \theta =\cos \frac{7\pi }{4}$
$\Rightarrow$ General value of $\theta =2n\pi \pm \frac{7\pi }{4},n\in I$