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Question

Solve for x:  tan1(x1)+tan1x+tan1(x+1)=tan13x. 


Solution

We have

tan1(x1)+tan1x+tan1(x+1)=tan1 3x ...............(1)

tan1(x1)+tan1(x+1)+tan1x=tan1 3x

[ Using tan1A+tan1B=tan1((A)+(B)1(A)(B))]

tan1((x1)+(x+1)1(x1)(x+1))+tan1x=tan1 3x

tan1(2x1x2+1)+tan1x=tan1 3x

tan1(2x2x2)+tan1x=tan1 3x

tan1(2x2x2+x12x2x2×x)=tan13x

tan1(2x+2xx32x22x2)=tan13x

tan1[4xx323x2]=tan13x

4xx323x2=3x

4xx3=6x9x3

8x32x=0

2x(4x21)=0

x=0 or 4x21=0

x=0 or 4x2=1

x=0 or x2=14

x=0 or x=±12

x=0,x=12,x=12

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