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MHT CET · Maths · Trigonometric Equations

The value of \(\theta\), satisfying both the equation \(\cos \theta=\frac{1}{\sqrt{2}}\) and \(\tan \theta=-1\) in \([0,2 \pi]\), is

  1. A \(\left(\frac{\pi}{4}\right)\)
  2. B \(\left(\frac{5 \pi}{4}\right)\)
  3. C \(\left(\frac{7 \pi}{4}\right)\)
  4. D \(\left(\frac{3 \pi}{4}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{7 \pi}{4}\right)\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \cos \theta=\frac{1}{\sqrt{2}} \text { and } \tan \theta=-1 \theta \in[0,2 \pi] \\ & \Rightarrow \theta=\frac{\pi}{4} \text { or } \frac{7 \pi}{4} \text { and } \theta=\frac{3 \pi}{4} \text { or } \frac{7 \pi}{4} \\ & \Rightarrow \theta=\frac{7 \pi}{4}\end{aligned}\)