Geometry
# Sum and Difference Trigonometric Formulas

Let $x = \sin\left(\sin^{-1} \left(\frac{3}{5}\right) + \tan^{-1} (2)\right)$. $x$ can be written in the form $\frac{a\sqrt{b}}{c}$, where $a, b$ and $c$ are positive integers, $a$ and $c$ are coprime and $b$ is not divisible by the square of any prime. What is the value of $a+b+c$?

**Details and assumptions**

$\sin^{-1}$ and $\tan^{-1}$ represent the inverse of the $\sin$ and $\tan$ function, and not the reciprocal.

Which of the following is equal to

$\arccos ( - x) ?$

If $x \in (0, \pi )$, which of the following is equal to

$\arctan ( \cot x) ?$