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The value of $\theta$, satisfying both the equation $\cos \theta=\frac{1}{\sqrt{2}}$ and $\tan \theta=-1$ in $[0,2 \pi]$, is
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Verified Answer
The correct answer is:
$\left(\frac{7 \pi}{4}\right)$
$\begin{aligned} & \cos \theta=\frac{1}{\sqrt{2}} \text { and } \tan \theta=-1 \theta \in[0,2 \pi] \\ & \Rightarrow \theta=\frac{\pi}{4} \text { or } \frac{7 \pi}{4} \text { and } \theta=\frac{3 \pi}{4} \text { or } \frac{7 \pi}{4} \\ & \Rightarrow \theta=\frac{7 \pi}{4}\end{aligned}$
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