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

Apr 20, 2016

$\pm \sqrt{3} \pm \left(\frac{3}{5}\right) \sqrt{10}$ = 3.629, - 1.653, 0.1653 and -3.629, nearly.

#### Explanation:

If sec is positive, tan could be positive or negative.
Let $a = a r c \sec 2. \sec a = 2 \mathmr{and} \tan a = \pm \sqrt{3}$.

So, the first term $\tan \left(a r c \sec 2\right) = \pm \sqrt{3}$

If cot is positive, cos could be positive or negative.
Let $b = a r c \cot 3. \cot b = 3 \mathmr{and} \cos b = \pm \frac{3}{\sqrt{10}}$.

So, the second term $- 2 \cos \left(a r c \cot 3\right) = - 2 \cos b = \pm \frac{6}{\sqrt{10}}$.

Remembering that the sign choice from $\pm$ is independent for each term,
the sum is $\pm \sqrt{3} \pm \frac{6}{\sqrt{10}} = \pm 3.629 , \pm 1.653$, nearly. . .