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Q.The function f(x)=cot⁡−1(1+sin⁡x+1−sin⁡x2)f(x)=\cot^{-1}\left(\dfrac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{2}}\right) simplifies to

a
π4+x2\dfrac{\pi}{4} + \dfrac{x}{2}
b
π4−x2\dfrac{\pi}{4} - \dfrac{x}{2}
c
x2\dfrac{x}{2}
d
π2−x2\dfrac{\pi}{2} - \dfrac{x}{2}

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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