KCET · Maths · Trigonometric Equations
\(\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]\) is
- A \(-\frac{3}{4}\)
- B \(-\frac{1}{2}\)
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\because \frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]\)
\(=\frac{d}{d x}\left(\cos \left(\cos ^{-1}\left(\frac{\sqrt{2+x}}{2}\right)\right)\right)^2\)
\(=\frac{d}{d x}\left(\frac{2+x}{4}\right)=\frac{1}{4}\)
\(=\frac{d}{d x}\left(\cos \left(\cos ^{-1}\left(\frac{\sqrt{2+x}}{2}\right)\right)\right)^2\)
\(=\frac{d}{d x}\left(\frac{2+x}{4}\right)=\frac{1}{4}\)
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