How Do You Simplify the Expression sin 3x cos x + cos 3x sin x?

[alliereid]

1. Determine an equivalent expression for sin 3x cos x + cos 3x sin x .
A. 4sin x
B. 2sin x cos x
C. 4sin x cos x
D. 2sin 2x cos 2x

2. sin(a+b) = sinacosb+cosasinb, sin2x = 2sinxcosx



3. This question appeared on a practice final I was attempting at. It's on a no calculator section so I'm having difficulty solving it without one. I got up to

sin 3x cos x + cos 3x sin x
= sin(3x + x)
= sin(4x)

The answer is 2sin 2x cos 2x, I know that sin2x = 2sinxcosx but I don't know how to expand it when sin2x becomes sin4x. It'd be great if someone could explain it. Thanks!

 

[rock.freak667]

sin2A=2sinAcosA

if A=2x

sin4x=2sin2xcos2x