Question

What does `tan(arcsec(2))-2cos(arc cot(3))` equal?

Answer 1

`+-sqrt 3+-(3/5)sqrt 10` = 3.629, - 1.653, 0.1653 and -3.629, nearly.

Explanation:

If sec is positive, tan could be positive or negative.
Let `a=arc sec 2. sec a=2 and tan a=+-sqrt 3`.

So, the first term `tan(arc sec 2)=+-sqrt3`

If cot is positive, cos could be positive or negative.
Let `b=arc cot 3. cot b=3 and cos b=+-3/sqrt 10`.

So, the second term `-2 cos(arc cot 3)=-2 cos b=+-6/sqrt 10`.

Remembering that the sign choice from `+-` is independent for each term,
the sum is `+-sqrt 3+-6/sqrt 10=+-3.629, +-1.653`, nearly. . .