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

Question

What identities is used to get the answer?

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Answer 1 · 2017-05-30T21:48:40

#2 sin(2 x) cos(2 x)#

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)#