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Question

12cos1(1x1+x)=

A
cot1x
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B
tan1x
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C
tan1x
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D
cot1x
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Solution

The correct option is B tan1x
Let x=tan2θθ=tan1x
Now, 12cos1(1x1+x)
=12cos1(1tan2θ1+tan2θ)
=12cos1cos2θ=2θ2=θ=tan1x.

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