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The most general value of $\theta$ which satisfies both the equations $\tan 8=-1$ and $\cos \theta=\frac{1}{\sqrt{2}}$ is
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Verified Answer
The correct answer is:
$2 n \pi+\frac{7 \pi}{4}$
Given trigonometric equations are
$\tan \theta=-1$
and
$\cos \theta=\frac{1}{\sqrt{2}}$
$\begin{array}{ll}\Rightarrow & \sin \theta=-1 / \sqrt{2} \\ \Rightarrow & \sin \theta=\sin \frac{7 \pi}{4} \\ \therefore & \theta=2 n \pi+\frac{7 \pi}{4}\end{array}$
$\tan \theta=-1$
and
$\cos \theta=\frac{1}{\sqrt{2}}$
$\begin{array}{ll}\Rightarrow & \sin \theta=-1 / \sqrt{2} \\ \Rightarrow & \sin \theta=\sin \frac{7 \pi}{4} \\ \therefore & \theta=2 n \pi+\frac{7 \pi}{4}\end{array}$
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