Question
Find maximum value of x for which 2tan−1x+cos−1(1−x21+x2) is independent of x.
Answer: Option A
:
A
Let x=tanθ,−π2<θ<π22θ+cos−1cos2θ
(i)0≤2θ<π2.2cos−1cos2θ=2θ
So given expression =4θ=4tan−1x
(ii)−π2<θ≤0⇒−π<2θ≤0cos−1cos2θ=−2θ
So, given expression becomes independent of θ
For −π2<θ≤0⇒−∞<x≤0
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:
A
Let x=tanθ,−π2<θ<π22θ+cos−1cos2θ
(i)0≤2θ<π2.2cos−1cos2θ=2θ
So given expression =4θ=4tan−1x
(ii)−π2<θ≤0⇒−π<2θ≤0cos−1cos2θ=−2θ
So, given expression becomes independent of θ
For −π2<θ≤0⇒−∞<x≤0
Was this answer helpful ?
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