COMEDK · Maths · 26. Differentiation
The derivative of \(y = \sin^2\left[\cot^{-1}\left(\sqrt{\dfrac{1-x}{1+x}}\right)\right]\) is
- A \(0\)
- B \(\dfrac{1}{2}\)
- C \(\dfrac{x}{2}\)
- D \(\dfrac{1-x}{2}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(\alpha = \cot^{-1}\left(\sqrt{\dfrac{1-x}{1+x}}\right)\) \(\Rightarrow \cot \alpha = \sqrt{\dfrac{1-x}{1+x}}\) The given function can be written as \(y = \sin^2 \alpha\). Using the trigonometric identity…
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