MHB Write a trigonometric expression as an algebraic expression

[Taryn1]

This problem probably should be easy, but I don't remember learning the basic way to do these problems: Write the trigonometric expression as an algebraic expression:

cos(arccos x + arcsin x)

The answer is zero, but I don't know how to get there...

 

[MarkFL]

Recall the identity:

$$\arccos(x)+\arcsin(x)=\frac{\pi}{2}$$

However, I suspect you are to use the angle-sum identity for cosine to write:

$$\cos\left(\arccos(x)+\arcsin(x)\right)=\cos\left(\arccos(x)\right)\cos\left(\arcsin(x)\right)-\sin\left(\arccos(x)\right)\sin\left(\arcsin(x)\right)$$

Can you continue?

 

[Taryn1]

Ohhhh, I think I get it now. Thanks!