Finding exact value of trigonometric functions I was wondering, how do I get the exact fraction (the value) of this trigonometric function: 
$$\cos\left(\sin^{-1}(12/13)+\sin^{-1}(4/5)\right)$$
Usually, I would evaluate the inverse sin in degree mode and multiply (by hand) by $\pi/180$.
But in this case, I don't get exact values of angles
For example :
$$\begin{eqnarray}
\sin^{-1}(12/13)=67,38...^\circ\\
\sin^{-1}(4/5)=53,13...^\circ
\end{eqnarray}
$$
Is there any way of doing it ?
Thank you!

HINT:
Let $A=\arcsin\dfrac{12}{13}$
Using the definition of Principal value of $\arcsin,0<A<\dfrac\pi2$
$\implies \cos A=+\sqrt{1-\sin^2A}=\dfrac5{13}$
