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Question

If cot1(1x+1)+cot1(1x1)=tan13xtan1x ,
then x=

A
±1/2
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B
1,±1/3
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C
2,±1
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D
1,±1/2
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Solution

The correct option is A ±1/2
cot1(1x+1)+cot1(1x1)=tan1(x+1)+tan1(x1)
=tan1(x+1+x11(x21))
=tan1(2x2x2) 1
and
tan13xtan1x=tan1(3xx1+3x2)=tan1(2x1+3x2) 2
equation 1 = 2
tan12x1+3x2=tan1(2x2x2)
1+3x2=2x2
4x2=1
x2=14
x=±12

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