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$If 0 < a < b < \frac{π}{b} and f (a, b) = \frac{\tan b - \tan a}{b - a}, then$

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fa,b≥2

fa,b>1

fa,b≤1

fa,b≤−2

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detailed solution

Correct option is B

consider the function f(x)=tan⁡x, defined on [a,b] such that a, b∈0,π2f′(c)=f(b)−f(a)b−a for some c∈(a,b)⇒sec2⁡C=tan⁡b−tan⁡ab−a⇒f(a,b)=sec2⁡C⇒f(a,b)>1 ∵sec2⁡C>1 as C∈(0,π/2)

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If 0<a<b<πb and f(a,b)=tan⁡b−tan⁡ab−a, then

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$If 0 < a < b < \frac{π}{b} and f (a, b) = \frac{\tan b - \tan a}{b - a}, then$