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Let \(f(x)=\cos \left(2{\tan }^{-1}\sin \left({\cot }^{-1}\sqrt{\frac{1-x}{x}}\right)\right)\), \(0 [JEE Main 2021, 26 A…

Q1

Let \(f(x)=\cos \left(2{\tan }^{-1}\sin \left({\cot }^{-1}\sqrt{\frac{1-x}{x}}\right)\right)\), \(0

[JEE Main 2021, 26 Aug (Shift 1)]

a

\((1-x{)}^{2}{f}^{'}(x)+2(f(x){)}^{2}=0\)

b

\((1-x{)}^{2}{f}^{'}(x)-2(f(x){)}^{2}=0\)

c

\((1+x{)}^{2}{f}^{'}(x)+2(f(x){)}^{2}=0\)

d

\((1+x{)}^{2}{f}^{'}(x)-2(f(x){)}^{2}=0\)

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