COMEDK · Maths · 23. Inverse Trigonometric Functions
Given \(\cos \left(\tan ^{-1} x\right)=\sin \left(\cot ^{-1} \dfrac{3}{4}\right)\), then the value of \(x\) is
- A \(\dfrac{1}{2}\)
- B \(\dfrac{4}{3}\)
- C \(\dfrac{3}{4}\)
- D 1
Answer & Solution
Correct Answer
(C) \(\dfrac{3}{4}\)
Step-by-step Solution
Detailed explanation
Let \(\theta = \tan^{-1} x\). Then \(\tan \theta = x\). Since \(\cos \theta = \dfrac{1}{\sqrt{1 + \tan^2 \theta}}\), we have \(\cos(\tan^{-1} x) = \dfrac{1}{\sqrt{1 + x^2}}\). Let \(\phi = \cot^{-1} \dfrac{3}{4}\). Then \(\cot \phi = \dfrac{3}{4}\), which implies…
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