QuestionSimplify the expression below in terms of $p$ and $q$. Your final answer should contain no trigonometric functions and should be written as an expression in $p$ and $q$ solely. $$\sin (\arcsin (p)+\arccos (q))$$

Studdy Solution
Substitute $\cos(\theta)$ and $\sin(\phi)$ back into the expression:
$\sin(\theta + \phi) = p \cdot q + \sqrt{1 - p^2} \cdot \sqrt{1 - q^2}$
The simplified expression in terms of $p$ and $q$ is:
$\boxed{p \cdot q + \sqrt{1 - p^2} \cdot \sqrt{1 - q^2}}$