Question

If $\cos \theta=-\frac{1}{\sqrt{2}}$ and $\tan \theta=1$, then the general value of $\theta$ is

• A. $2 n \pi+\frac{\pi}{4}, n=0,1,2,3 . \ldots \ldots$.
• B. $(2 n+1) \pi+\frac{\pi}{4}, n=0,1,2,3 \ldots \ldots \ldots$
• C. $n \pi+\frac{\pi}{4}, n=0,1,2,3 \ldots \ldots \ldots$
• D. $n \pi \pm \frac{\pi}{4}, n=0,1,2,3 \ldots \ldots$

Answer 1

Answer: (B)

$\cos \theta=\frac{-1}{\sqrt{2}}$ and $\tan \theta=1$
$\Rightarrow \cos \theta=-\cos \frac{\pi}{4}$ and $\tan \theta=\tan \frac{\pi}{4}$
$\Rightarrow \cos \theta=\cos \left(\pi+\frac{\pi}{4}\right)$ and $\tan \theta=\tan \left(\pi+\frac{\pi}{4}\right)$
[ $\because$ in IIIrd quadrant, cosine is negative and tangent is positive]
$\Rightarrow \theta=(2 n+1) \pi+\frac{\pi}{4}, n=0,1,2,3, \ldots$