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Question

The value of limx12xcos(sin1x)1tan(sin1x) is

A
12
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B
12
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C
2
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D
2
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Solution

The correct option is C 12
limx12xcos(sin1x)1tan(sin1x)
Let sin1x=θ
Then,x=sinθ
Also, x12θπ4
So, limx12xcos(sin1x)1tan(sin1x)=limθπ4sinθcosθ1tanθ
=limθπ4(sinθcosθ)(cosθsinθ)cosθ
=limθπ4cosθ=12


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