Trigonometric identity forced oscillations

[Gyroscope]

Homework Statement

http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf

http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf

Question A- (b)

They use some trigomentric identity that I don't understand, which one is it?

Thanks in advance.

Homework Equations

The Attempt at a Solution

 

[cristo]

Well, you've got an expression that's in the form sinAsinB; so you look to use the formula cos(A-B)=cosAcosB+sinAsinB.

From this, you know that $$\cos\{\omega_it-\phi-\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)+\sin\{\omega_i t-\phi\}\sin(\omega t)$$. You can work out the similar expression that $$\cos\{\omega_it-\phi+\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)-\sin\{\omega_i t-\phi\}\sin(\omega t)$$ Then subtract the second from the first.