- #1
neutrino2063
- 7
- 0
I need to somehow simplify:
[tex]\frac{1}{B^2}=\frac{1+\cos{2\alpha}}{2k_1}+\frac{\sin{2\alpha}}{2k_2}+\frac{\alpha}{k_2}[/tex]
to:
[tex] B=\sqrt{\frac{2}{L}}\sqrt{\frac{\beta}{1+\beta}} [/tex]
Where:
[tex]\alpha=\frac{L}{2}k_2 [/tex] and [tex]\beta=\frac{L}{2}k_1 [/tex]
And [tex]\beta[/tex] is also defined transcendentally:
[tex]\beta=\alpha\tan{\alpha}[/tex]
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.
[tex]\frac{1}{B^2}=\frac{1+\cos{2\alpha}}{2k_1}+\frac{\sin{2\alpha}}{2k_2}+\frac{\alpha}{k_2}[/tex]
to:
[tex] B=\sqrt{\frac{2}{L}}\sqrt{\frac{\beta}{1+\beta}} [/tex]
Where:
[tex]\alpha=\frac{L}{2}k_2 [/tex] and [tex]\beta=\frac{L}{2}k_1 [/tex]
And [tex]\beta[/tex] is also defined transcendentally:
[tex]\beta=\alpha\tan{\alpha}[/tex]
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.
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