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**HallsofIvy** Or "rationalize the denominator" by multiplying numerator and denominator by the conjugate of the denominator:

$\displaystyle \left(\frac{-cos(\alpha)+ isin(\alpha)}{cos(\alpha)+ isin(\alpha)}\right)\left(\frac{cos(\alpha)- isin(\alpha)}{cos(\alpha)- isin(\alpha)}\right)$

$\displaystyle = -cos^2(\alpha)+ sin^2(\alpha)+ 2sin(\alpha)cos(\alpha)$.

Now, what about that left side? $\displaystyle cis(\pi- 2\alpha)= cos(\pi- 2\alpha)+ isin(\pi- 2\alpha)= -cos(2\alpha)+ isin(2\alpha)$

So what are $\displaystyle cos(2\alpha)$ and $\displaystyle sin(2\alpha)$?