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The function \(f(x)\), that satisfies the condition \(f(x)=x+{\int }_{0}^{\pi /2}\sin x\cdot \cos yf(y)dy\) is: [JEE Mai…

Q1

The function \(f(x)\), that satisfies the condition \(f(x)=x+{\int }_{0}^{\pi /2}\sin x\cdot \cos yf(y)dy\) is:

[JEE Main 2021, 1 Sep (Shift 2)]

a

\(x+\frac{2}{3}(\pi-2) \sin x\)

b

\(x+(\pi+2) \sin x\)

c

\(x+\frac{\pi}{2} \sin x\)

d

\(x+(\pi-2) \sin x\)

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