COMEDK · Maths · 23. Inverse Trigonometric Functions
\(\text { Evaluate: } \cot ^{-1}\left(-\dfrac{3}{\sqrt{3}}\right)-\sec ^{-1}\left(-\dfrac{2}{\sqrt{2}}\right)-\operatorname{cosec}^{-1}(-1)-\tan ^{-1}(1)\)
- A \(-\dfrac{2 \pi}{3}\)
- B 0
- C \(\dfrac{\pi}{3}\)
- D \(\dfrac{\pi}{6}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
The given expression is \(E = \cot ^{-1}\left(-\dfrac{3}{\sqrt{3}}\right) - \sec ^{-1}\left(-\dfrac{2}{\sqrt{2}}\right) - \operatorname{cosec}^{-1}(-1) - \tan ^{-1}(1)\). Simplify the arguments: \(\dfrac{3}{\sqrt{3}} = \sqrt{3}\) and \(\dfrac{2}{\sqrt{2}} = \sqrt{2}\). Evaluate…
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