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Question

cos1x=tan11x2x, then:

A
XR
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B
x1,x0
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C
0<x1
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D
None of these
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Solution

The correct option is C 0<x1
Putting θ=cos1x in R.H.S., we have
R.H.S =tan11x2x=tan11cos2θcosθ(0θπ)=tan1sinθcosθ=tan1tanθ=θ=cos1x when π2<θ<π2
i.e., when 0θ<π2
i.e., when 0<cosθ1 i.e., 0<x1.

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