proving identities

[xc630]

Hello i need major help proving this identity.

sin 4x = 4 sinx cos x cos 2x

Please Help!

 

[stapel]

Are you allowed to use the double-angle identities for sine and cosine?

Thank you.

Eliz.

 

[xc630]

yes i know sin 2 A = 2 sin a Cos A and cos 2A can equal one of these:
Cos^2A-Sin^2A
1-2Sin^2A
2Cos^2A

In my problem I think 4 sinx cos x would equal sin4x but I don't know what to do fromt here

 

[Mrspi]

Hello i need major help proving this identity.

sin 4x = 4 sinx cos x cos 2x

Please Help!

Generally, I'm a big fan of working with the more complicated side of an identity (which is the right-hand side). But sometimes, it's easier to work with the simpler side, and that is what I am going to do:

Here's what we will do to the left side:
sin4x
sin 2(2x)
2 sin 2x cos 2x
But sin 2x is 2 sin x cos x, so we have
2(2 sin x cos x) cos 2x
4 sin x cos x cos 2x

And that is what is on the right side......

I hope this helps you.

 

[xc630]

thank you