MHT CET · Maths · Trigonometric Ratios & Identities
If \(\tan \theta=2\) and \(\theta\) lies in the third quadrant, then the value of \(\sec \theta\) is
- A \(-\sqrt{5}\)
- B \(\sqrt{3}\)
- C \(-\sqrt{2}\)
- D \(\sqrt{5}\)
Answer & Solution
Correct Answer
(A) \(-\sqrt{5}\)
Step-by-step Solution
Detailed explanation
\(\sec ^{2} \theta=1+(2)^{2}=5\)
\(\therefore \sec \theta=-\sqrt{5}\) \(\quad\quad\left[\because \theta\right.\) lies in \(3^{\text {nd }}\) quadrant. \(]\)
\(\therefore \sec \theta=-\sqrt{5}\) \(\quad\quad\left[\because \theta\right.\) lies in \(3^{\text {nd }}\) quadrant. \(]\)
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