Expert: Steve Holleran - 7/17/2008

Question
How do i verify each identity?
sin(2x)= 2 sin(x)cos(x)

Answer
Hi Juan,


I don't know exactly what you mean by verifying this, because it is already one of the fundamental double-angle identities.  But if you want to derive it, it comes from the sum formula for the sine:

              sin(x + y) = sin x cos y + cos x sin y

Now, if you replace y with x, you have

    sin(x + x) = sin(2x) = sin x cos x + cos x sin x

Notice now that the terms on the right are the same, so you have

                 sin(2x) = 2 sin x cos x


Hope this is what you needed.

Steve