If a = _ n _ k=1 ^ n 2n/(n^ 2 + k^ 2 ) and f(x) = (1 − cos x)/(1 + cos x)), x (0, 1), then

JEE Main 2022 Mathematics question

If and − cos x)/(1 + cos x)), x (0, 1), then

Answer: (3)

a = lim 2/(1 + . Also − cos x)/(1 + cos x)) = tan(x/2) for x (0, 1), i.e. cosec x − cot x. So f(a/2) =

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Question ID VK-025173