~SOME INVERSE TRIG IDENTITIES~

~These are very useful when computing values on your calculator,
  since there are NO buttons for inverse sec, inverse csc, and inverse cot.
  (some more advanced calculators do have them)
  Expressing them in terms of the inverse cos, inverse sin, and inverse tan
  is the best way to do compute them

~Make sure you keep a close eye on your mode when doing a calculation
  involving trig functions. Many mistakes occur here.
(press mode & use Radian or Degree)

~I will assume, in the following proofs, permitted values for x are used.

~If, by mistake, you use a value outside of their domains, your calculator
will explode.

1)  sec^-1(x)=cos^-1(1/x)

     Proof:   Let y = sec^-1(x) then sec(y)=x then 1/cosy = x/1
                  then cos(y) =1/x then y=cos^-1(1/x)
                  hence,    sec^-1(x)=cos^-1(1/x)

2)  csc^-1(x)=sin^-1(1/x)

     Proof:   Let y=csc^-1(x) then csc(y)=x then 1/sin(y)=x/1
                 then sin(y)= 1/x then y=sin^-1(1/x)
                  hence,  csc^-1(x)=sin^-1(1/x)

3)  cot^-1(x)=tan^-1(1/x)

     Proof:   Let y = cot^-1(x) then cot(y)=x then 1/tan(y)=x/1
                  then tan(y)=1/x then y=tan^-1(1/x)
                  hence,  cot^-1(x)=tan^-1(1/x)

Example: Say you would like the value of sec^-1(-2).
Since sec^-1(-2) = cos^-1(1/-2), Press 2nd Cos & enter -1/2. You should get 2.0944 for a value (4 decimal places).