Given, 0<x<1
2tan−1(1+x1−x)=cos−1(1+x21−x2)
Put x=tan(θ);0<θ<4π
2tan−1(1+tanθ1−tanθ)=cos−1(1+tan2θ1−tan2θ)
⇒2tan−1(tan(4π−θ))=cos−1(cos2θ)
2(4π−θ)=2θ⇒θ=8π
Put θ=tan−1x we get,
x=tan8π∴x=2−1≃0.414<21
Let S=x∈R:0<x<1and2tan−1(1+x1−x)=cos−1(1+x21−x2). If n(S) denotes the number of elements in S then :
Held on 1 Feb 2023 · Verified 6 Jul 2026.
n(S)=2 and only one element in S is less then 21
n(S)=1 and the element in S is more than 21
n(S)=1 and the element in S is less then 21
n(S)=0
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