1. ## Cosine Transform Question

Hi,

I'm trying to solve:

$\displaystyle f(t) = cos(\omega t) : 0 < t < T$

And I've got as far as this:

$\displaystyle \frac{1}{\omega}(\frac{\omega T}{2}+\frac{sin2 \omega T}{4})$

$\displaystyle \frac{\omega T}{2 \omega}+\frac{1}{4 \omega}sin2 \omega T$

$\displaystyle \frac{T}{2}+\frac{1}{4 \omega}sin2 \omega T$

However I don't understand how to algebraically solve this for the given answer:

$\displaystyle \frac{T}{2}(1+\frac{sin2 \omega T}{2 \omega T})$

I don't see how the right term has obtained the denominator $\displaystyle T$ underneath $\displaystyle sin2 \omega T$

I'm wondering if my tutor has made a mistake?

Any help would be appreciated.