Solving Simple Trig Identities Homework Problem

[Sneaky07]

Homework Statement

Simplify this expression:
f(t) = sin($$\beta$$t)*cos($$\beta$$t)

Homework Equations

Identities

The Attempt at a Solution

I started out by doing sin($$\beta$$t)*sin($$\beta$$t+$$\pi$$/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original formula which it should. Anyone have an idea? Just the start would be MUCH appreciated.

 

[Bohrok]

You have f(x) but no x anywhere on the other side. What is the variable and what is constant?

 

[Sneaky07]

Sorry about that. It should be f(t).

 

[Bohrok]

The first thing that came to mind was 2sinxcosx = sin2x

 

[Sneaky07]

Ahh! I think that is what I needed. If 2sin(x)cos(x)=sin(2x) then I can multiply both sides by 2 which gives 2f(t)=2sin($$\beta$$t)cos($$\beta$$t). After, just carry the 2 over so you get f(t)=(1/2)sin(2$$\beta$$t). Thanks man!