Equation With Sine Expressions, LLC resonant converter equations

[treez]

Hello,

How do you derive the equation at the bottom left of page three of this.....

http://www.fairchildsemi.com/an/AN/AN-4151.pdf

...that is, how does the expression containg alll the w's come out from the expression containg a sine in the numerator and denominator?..

..is there some standard substitution you can do for the sine expressions?

[Sch3mat1c]

Substitution, cancellation, substitution again.

[Village Idiot]

The applicable substitution appears to be:

sin(x)/sin(x)=1

[treez]

Thanks, i cant find them in maths book, do you just call them "sine substitutions"

[Village Idiot]

Try looking for "trigonometric identities"

Lot's of info here:
http://en.wikipedia.org/wiki/Trigonometric_identities
Actually, it's a bit of information overload.

Generally, useful in electronics are the sum-to-product and product-to-sum transformations, which you can find on that page.

What I mentioned in my previous post doesn't even qualify as a trigonometric substitution. It was simply two identical terms in the numerator and denominator which automatically cancel out. It had nothing to do with the fact that it was a sine function.