Consider, $$\frac{e^{i\theta/2}-e^{-i\theta/2}}{e^{i\theta/2}+e^{-i\theta/2}}$$ Can this be reduced to $$\frac{e^{i\theta}-1}{e^{i\theta}+1}$$ If so how? What identity to use?
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10Multiply the numerator and denominator by $e^{i\theta/2}$. Note the first form tells you this ratio is $i\tan(\theta/2)$ which is nice – FShrike Jan 12 '23 at 18:11
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Converting the denominator of the second formula to a real number gives you a nice expression in terms of $\sin\theta$ and $\cos\theta$. – eyeballfrog Jan 12 '23 at 18:24