Solve: 2 arctan ( 1 2 ) + arctan ( 1 7 ) = ?

Question

Solve:       2          arctan              (                  1          2                )              +          arctan              (                  1          7                )              =  ?

nelagodafsed · Accepted Answer

Knowing this,                              (          1          )                a        r        c                  tan          x                +        a        r        c                  tan          y                =        a        r        c                  tan                      (                                          x                +                y                                            1                -                x                ⋅                y                                      )                               ,                     x        ⋅        y        &amp;lt;        1            Let  ,        A    =    2    a    r    c          tan              (                  1          2                )              +    a    r    c          tan              (                  1          7                )            Using  (1) we get ,                    2        a        r        c                  tan                      (                          1              2                        )                                =    a    r    c          tan              (                  1          2                )              +    a    r    c          tan              (                  1          2                )                                2        a        r        c                  tan                      (                          1              2                        )                                =    a    r    c          tan              (                                            1              2                        +                          1              2                                            1            -                          1              2                        ⋅                          1              2                                      )              ,        x    ⋅    y    =          1      2        ⋅          1      2                          2        a        r        c                  tan                      (                          1              2                        )                                =    a    r    c          tan              (                  1                      1            -                          1              4                                      )                                2        a        r        c                  tan                      (                          1              2                        )                                =    a    r    c          tan              (                  1                                    3              4                                      )                                2        a        r        c                  tan                      (                          1              2                        )                          =        a        r        c                  tan                      (                          4              3                        )                              Then,      A    =                  a        r        c                  tan                      (                          4              3                        )                                +    a    r    c          tan              (                  1          7                )              →                  A        p        p        l        y                  (          1          )                          A    =    a    r    c          tan              (                                            4              3                        +                          1              7                                            1            -                          4              3                        ⋅                          1              7                                      )              ,    x    ⋅    y    =          4      3        ⋅          1      7        =          4      21        &amp;lt;    1        A    =    a    r    c          tan              (                              28            +            3                                21            -            4                          )                  A    =    a    r    c          tan              (                  31          17                )

Solve: 2arctan(1/2)+arctan(1/7)=?

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Answer & Explanation

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