There exists a positive real number x satisfying cos(tan−1x)=x. Then the value of cos–1(x22) is
A
2π5
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B
4π5
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C
π10
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D
π5
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Solution
The correct option is A2π5 Let tan−1(x)=θ ⇒tanθ=x
By right angled triangle, cosθ=1√1+x2 ⇒1√1+x2=x ⇒x2(1+x2)=1⇒x4+x2−1=0⇒x2=−1±√52
But x2 cannot be negative. x2=√5−12 ⇒x22=√5−14