The integral ${\int }_{1/4}^{3/4}\cos \left(2co{t}^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx$ is equal to: [JEE Main 2024, 09 Apr (Shift 2)]

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The integral \({\int }_{1/4}^{3/4}\cos \left(2co{t}^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx\) is equal to: [JEE Main 2024, 0…