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Question: Answered & Verified by Expert
The value of $\theta$, satisfying both the equation $\cos \theta=\frac{1}{\sqrt{2}}$ and $\tan \theta=-1$ in $[0,2 \pi]$, is
MathematicsTrigonometric EquationsMHT CETMHT CET 2022 (06 Aug Shift 1)
Options:
  • A $\left(\frac{\pi}{4}\right)$
  • B $\left(\frac{5 \pi}{4}\right)$
  • C $\left(\frac{7 \pi}{4}\right)$
  • D $\left(\frac{3 \pi}{4}\right)$
Solution:
2625 Upvotes 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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