why are some trigonometric substitutions not explained in books? In some books I find trigonometric substitution explained for only 3 cases
in which one is: 
$$\sqrt{a^2-x^2}=acos\theta$$
but so far i've never seen this one
$$\sqrt{a^2-x^2}=asin\theta$$
I believe it's a legit substitution since  you can choice where to put the angle in the triangle. Why does nobody explain this one?

Either one is fine. Perhaps $x=\sin\theta$ is the preferred substitution because the derivative is simple ($\text{d}x = \cos\theta\text{ d}\theta$), whereas for the other substitution the derivative will involve a negative sign.
