COMEDK · Maths · 23. Inverse Trigonometric Functions
\(\text { The value of } \sin ^{-1}\left[\cot \left(\dfrac{1}{2} \tan ^{-1} \dfrac{1}{\sqrt{3}}+\cos ^{-1} \dfrac{\sqrt{12}}{4}+\sin ^{-1} \dfrac{1}{\sqrt{2}}\right)\right]
\) is
- A \(\dfrac{\pi}{6}\)
- B 0
- C \(\dfrac{\pi}{4}\)
- D \(\dfrac{\pi}{2}\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Let the expression inside the cotangent be \(\theta\). \(\theta = \dfrac{1}{2} \tan^{-1} \left(\dfrac{1}{\sqrt{3}}\right) + \cos^{-1} \left(\dfrac{\sqrt{12}}{4}\right) + \sin^{-1} \left(\dfrac{1}{\sqrt{2}}\right)\) We know that…
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