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How solve equation arctg1+arctg2+arctgx=pie?

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lemong | Student, Undergraduate | (Level 1) Honors

Posted August 3, 2013 at 4:26 PM via web

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How solve equation arctg1+arctg2+arctgx=pie?

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aruv | High School Teacher | (Level 2) Valedictorian

Posted August 3, 2013 at 4:40 PM (Answer #1)

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We have

`tan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy))`

Apply this formula

`tan^(-1)1+tan^(-1)2+tan^(1)x`

`=tan^(-1)((1+2)(1-1xx2))+tan^(-1)x`

`=tan^(-1)(3/(1-2))+tan^(-1)x`

`tan^(-1)(-3)+tan^(-1)x=tan^(-1)((-3+x)/(1-(-3)x))`

`=tan^(-1)((x-3)/(1+3x))`

`Thus`

`tan^(-1)((x-3)/(1+3x))=pi`

`(x-3)/(1+3x)=tan(pi)`

`(x-3)/(1+3x)=0`

`=> x-3=0`

`=>x=3`

ans.

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