Homework Help: Trig Simplification

1. Oct 30, 2008

neutrino2063

I need to somehow simplify:

$$\frac{1}{B^2}=\frac{1+\cos{2\alpha}}{2k_1}+\frac{\sin{2\alpha}}{2k_2}+\frac{\alpha}{k_2}$$

to:

$$B=\sqrt{\frac{2}{L}}\sqrt{\frac{\beta}{1+\beta}}$$

Where:

$$\alpha=\frac{L}{2}k_2$$ and $$\beta=\frac{L}{2}k_1$$

And $$\beta$$ is also defined transcendentally:

$$\beta=\alpha\tan{\alpha}$$

Any ideas would be appreciated, I see no way of getting rid of the trig functions. I've tried looking for identities and even given it to mathematica; it seems to me I'm missing some sort of special trick.

Last edited: Oct 31, 2008
2. Oct 31, 2008

Staff: Mentor

Is it a typo that alpha and beta are equal? It seems an unnecessary complication to add another variable if it's not needed. Otherwise I would just start substituting things into the right side of your first equation and see where that takes me.

3. Oct 31, 2008

neutrino2063

Ah, it is... thanks, it's fixed now alpha should be (L/2)*k2

4. Oct 31, 2008

Staff: Mentor

Now replaces cos(2 alpha) and sin(2 alpha) using the double-angle identities, and use your other two relationships to get rid of alpha to see if you can make the right side look like the left.