CVEL4

Find where $\sin z = \cos z\,$ .

$\frac{e^{iz}-e^{-iz}}{2i} = \frac{e^{iz}+e^{-iz}}{2}\,$

$e^{iz} (1-i) = e^{-iz} (1+i)\,$

$e^{2iz} = \frac{1+i}{1-i} \cdot \frac{1+i}{1+i} = \frac{(1+i)^2}{2} = i = e^{i\frac{\pi}{2}}\,$

Therefore

$2z = \frac{\pi}{2} + k2\pi, k\isin \mathbb{Z}\,$

$z = \frac{\pi}{4} + k\pi, k\isin \mathbb{Z}\,$