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Question

cos1x=tan12x1+x2, then:

A
x ϵ R
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B
1x1,x0
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C
0<x1
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D
1 x<0
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Solution

The correct option is C 0<x1

Puttting θ=cos1x in RHS, we have
R.H.S =tan11x2x
=tan11cos2θcosθ(0θπ)
=tan1sinθcosθ=tan1tanθ
=θ=cos1x when π2<θ<π2
i,e., when0θπ2
i.e., when 0<cosθ1 i.e., 0<x1

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