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I am not able to go from

$ 4r (1-\theta) sin^{2}(\frac{\omega}{2})-4r sin^{2}(\frac{\omega}{2}) <2$

simplifies to

$ 2r(1-\theta)-2r \theta) sin^{2}(\frac{\omega}{2}) < 1 $

I am not able to follow from here, can anyone explain?

thank you.

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  • $\begingroup$ Divide the whole thing by 2 and factor out the $sin^2$ on the LHS. You are missing a parenthesis in the second line. And you are probably missing a $\theta$ in the first one (or you've added an extra one in the second one). $\endgroup$ – NickD May 12 '17 at 18:10
  • $\begingroup$ Multiply the whole inequality by $\;\cfrac12\;$.,..and in the second line erase that right parentheses and that $\;\theta\;$ there. $\endgroup$ – DonAntonio May 12 '17 at 18:10
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$$\sin^2(\omega/2)$$ is a common factor, thus you can write $$(4r(1-\theta)-4r)\sin^2(\omega/2)<2$$

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