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

Q1

Let \(f\left(x\right)=\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

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

b

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

c

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

d

\( \left.(1+x)^{2} f^{\prime}(x)-2(f x)\right)^{2}=0 \)

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