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Question

Solve tan1(1x1+x)=12tan1x,(0<x<1)

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Solution


tan1(1x1+x)=12tan1x2tan1(1x1+x)=tan1x
tan1⎜ ⎜2(1x1+x)1(1x1+x)2⎟ ⎟=tan1xtan1(1x22x)=tan1x
1x22x=x1x2=2x2x=±13
Neglecting x=13
We get x=13

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