CPM Homework Help : INT3 Problem 12-110

Show how to derive the double angle formulas for $\sin(2x)$ and $\cos(2x)$ by substituting $x$ for both $α$ and $β$ in the formulas for $\sin(α+β)$ and $\cos(α+β)$ , then simplifying.

Step 1:

$\sin(x+x)$

Hint:

What is this equivalent to? How can you change it?

Partial Answer:

$\sin (x+x)\ =\ \sin (x)\cos (x)+\sin (x)\cos (x)\ =\ 2\sin (x)\cos (x)$

More Help:

Now use the same method to find the double angle formula for $\cos(2x)$ .