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

What identities is used to get the answer?

What identities is used to get the answer?

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May 30, 2017

Answer:

#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)#

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