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Question

If tan(cos1x)=sin(cot112), then x =


A

±53

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B
±53
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C
±53
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D

None of these

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Solution

The correct option is B ±53
Given that tan{cos1(x)}=sin(cot112)
Let cot112=ϕ12=cotϕ
sinϕ=11+cot2 ϕ=25
Let cos1x=θsec θ1xtan θ=sec2 θ1
tan θ=1x21tan θ=1x2x
So,tan{cos1(x)}=sin(cot112)
tan(tan11x2x)=sin(sin125)1x2x=25(1x2)5=2x
Squaring both sides, we get x=±53.

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