1. Show that, for acute $\theta ,$

   $$\cos \theta =\sqrt{1-{\sin }^2\theta }$$

   and hence show that

   $$\cos (\arcsin y)=\sqrt{1-y^2}$$

2. Express

   $$\arcsin \alpha +\arcsin \beta$$

   as a single $\arcsin .$

3. Express

   $$\arccos \alpha +\arccos \beta$$

   as a single $\arccos .$

For (a), recall that

Again for (a), $\sin$ and $\arcsin$ are inverse functions, so $\sin (\arcsin \theta )=\theta .$

For (b), let $y=\arcsin \alpha +\arcsin \beta$ and find