How to simplify Cotangent(Arcsin)?

Question

Trinity Mack · Accepted Answer

d                        d          x                            [              cos                  (                      arcsin            x                    )                    ]        =    -          sin              (                  arcsin          x                )              ⋅          1                                    1            -                          x              2                                            =    -          x                        1          -                      x            2                                    u    =    1    -          x      2      ,       d    u    =    -    2    x          d      x            ∫                  -        x                                          1            -                          x              2                                                  d      x        =          1      2        ∫                  -        2        x                                          1            -                          x              2                                                  d      x            =          1      2        ∫          1                                    u                                d    u        =          1      2        ∫          u              -                  1          2                      d    u        =          1      2        ⋅          [      2              u            ]        =          u        =                  1        -                  x          2                          ∫          {              d                              d            x                                      [                  cos                      (                          arcsin              x                        )                          ]            }              d      x        =          cos              (                  arcsin          x                )                        cot              (                  arcsin          x                )              =                            cos                      (                          arcsin              x                        )                                                sin                      (                          arcsin              x                        )                                    ⇒                            cos                      (                          arcsin              x                        )                              x        =                            1          -                      x            2                              x

How to simplify Cotangent(Arcsin)?

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