What is sin(4x) in terms of sin(2x) and cos(2x)?

What identities is used to get the answer?

1 Answer
May 30, 2017

2 sin(2 x) cos(2 x)

Explanation:

We have: sin(4 x)

= sin(2 x + 2 x)

Let's apply the angle sum identity for sin(x); sin(alpha + beta) = sin(alpha) cos(beta) + cos(alpha) sin(beta):

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

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

= 2 sin(2 x) cos(2 x)