How the 2nd equation shown below is arrived to from the first one?

[Lunat1c]

Hi,

Can someone please show me how the 2nd equation shown below is arrived to from the first one?

http://img263.imageshack.us/img263/126/voltages.jpg

I started with:

$$V_R = \frac{\sqrt(2)E}{\pi} \Bigg[\bigg(-cos(\omega t)\bigg)_{\alpha}^{\beta} - sin(\beta)\omega CR\bigg(exp\bigg({-\frac{\omega t - \beta}{\omega CR}}\bigg)_{\beta}^{\pi+\alpha}\Bigg]$$

$$V_R = \frac{\sqrt(2)E}{\pi} \Bigg[-cos(\beta)+cos(\alpha) - sin(\beta)\omega CR\bigg(exp\bigg({-\frac{\pi+\alpha-\beta}{\omega CR}}\bigg) - 1\bigg)\Bigg]$$

I can't figure out how to continue from there.. there must be some kind of identity that I can use which I'm not familiar with

 

[hunt_mat]

It looks as if there is an i missing from the exponential.

 

[Lunat1c]

That thought did cross my mind however there shouldn't be any 'i' ($$\sqrt-1$$)

 

[hunt_mat]

From what I can see, there is no way of getting from the top to the bottom. One reason is that the double angle formula gives the product of trig functions, and you clearly don't have that in the top formula.