Is there any formula for arctan ⁡ ( a + b )

Question

Is there any formula for   arctan  ⁡      (    a    +    b    )

barene55d · Accepted Answer

The following formula is well known  arctan  ⁡  (  a  )  +  arctan  ⁡  (  b  )  =  arctan  ⁡      (                  a        +        b                    1        −        a        b              )  (of course up to a multiple of   π with   a  b  ≠  1). Then  arctan  ⁡  (  a  +  b  )  +  arctan  ⁡  (  a  −  b  )  =  arctan  ⁡      (                  2        a                    1        −                  a          2                +                  b          2                      )    arctan  ⁡  (  a  +  b  )  −  arctan  ⁡  (  a  −  b  )  =  arctan  ⁡      (                  2        b                    1        +                  a          2                −                  b          2                      )  Hence we have                    2        arctan        ⁡        (        a        +        b        )                            =        arctan        ⁡                  (                                    2              a                                      1              −                              a                2                            +                              b                2                                              )                +        arctan        ⁡                  (                                    2              b                                      1              +                              a                2                            −                              b                2                                              )                                    arctan        ⁡        (        a        +        b        )                            =                  1          2                arctan        ⁡                  (                                    2              a                                      1              −                              a                2                            +                              b                2                                              )                +                  1          2                arctan        ⁡                  (                                    2              b                                      1              +                              a                2                            −                              b                2                                              )

Is there any formula for arctan(a+b)

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