### Home > INT3 > Chapter 12 > Lesson 12.2.3 > Problem12-110

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. Homework Help ✎

$\sin(x+x)$

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

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

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