Core Maths 4: Trig...using the triple angle formulae to show that...

Hi there

I have this question:

Choosing suitable values of A and B, show that sin 3θ + sin θ = 2 sin 2θ cos θ

I have been at this one for hours, please could someone give me a nudge in the right direction, maybe show me the first 2 steps that you would take, please do not give me a full solution!

Many thanks
Jackie

Hi there

I have this question:

Choosing suitable values of A and B, show that sin 3θ + sin θ = 2 sin 2θ cos θ

I have been at this one for hours, please could someone give me a nudge in the right direction, maybe show me the first 2 steps that you would take, please do not give me a full solution!

Many thanks
Jackie

3=2+1

split up the $\sin{3 \theta}$ using that.

Then you should be able to get it to look like $\sin{2 \theta} \cos{\theta} + \sin{\theta} ( \cos{2 \theta} + 1)$

Next use an identity for $\cos{2 \theta}$ and rewrite the 1 in terms of trig functions. You should be able to cancel some tuff and make it look like

$\sin{2 \theta} \cos{\theta} + 2\sin{\theta} \cos^2{\theta}$

which just needs you to apply one final identity....