Express sec − 1 ⁡ ( x ) in terms of cos − 1 ⁡ ( x )

Question

Express       sec          −      1        ⁡  (  x  ) in terms of       cos          −      1        ⁡  (  x  )

Krystal Dillon · Accepted Answer

sec          −      1        ⁡  (  x  )  =      cos          −      1        ⁡            (                  1      x                  )

Cale Terrell · Accepted Answer

If  sec  ⁡  θ  =            2              3            then  cos  ⁡  θ  =            1              sec        ⁡        θ              =                    3            2      so  θ  =      sec          −      1        ⁡      (                  2                  3                      )    =      cos          −      1        ⁡      (                            3                2              )  In this case,   θ  =  ±      30    ∘    +  n  ×      360    ∘  , where n is any integer.In general, if   sec  ⁡  θ  =  x then   cos  ⁡  θ  =  1      /    x, so  θ  =      sec          −      1        ⁡  x  =      cos          −      1        ⁡      (                  1        x              )

Express sec^(−1)(x) in terms of cos^(−1)(x)

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