show that tan^1(a+b/1+ab)+tan^1(b-c/1+bc)+tan^1(c-a/1+ca)=0​

Question

show that
tan^1(a+b/1+ab)+tan^1(b-c/1+bc)+tan^1(c-a/1+ca)=0​

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Isabella 2 weeks 2021-11-23T02:19:46+00:00 1 Answer 0 views 0

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    2021-11-23T02:20:55+00:00

    Answer:

    Step-by-step explanation:

    LHS = tan^{-1}(\frac{a-b}{1+ab}) + tan^{-1}(\frac{b-c}{1+bc})+ tan^{-1}(\frac{c-a}{1+ca})

           =tan^{-1}a -tan^{-1}b+tan^{-1}b-tan^{-1}c+tan^{-1}c-tan^{-1}a

           =0

           =RHS.

    FORMULA:      tan^{-1}x -tan^{-1}y=tan^{-1}(\frac{x-y}{1+xy})

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