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Question

If tanāˆ’11āˆ’x1+x=12tanāˆ’1x, then x=

A
1
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B
3
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C
13
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D
None of these
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Solution

The correct option is C 13
tan11x1+x=12tan1x2tan1(1x1+x)=tan1x
tan1⎜ ⎜2(1x1+x)1(1x1+x)2⎟ ⎟=tan1x2(1x)(1+x)(1+x)2(1x)2=x
2(1x2)4x=x22x2=4x2
2=6x2x=13

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