Davion Harding

2022-06-26

Exact value of ${\mathrm{cos}}^{2}\left(\frac{\pi }{8}\right)+{\mathrm{sin}}^{2}\left(\frac{15\pi }{8}\right)?$

Lisbonaid

Expert

Notice that $\frac{15\pi }{8}=2\pi -\frac{\pi }{8}$. So $\mathrm{sin}\frac{15\pi }{8}=-\mathrm{sin}\frac{\pi }{8}$. Your expression then reduces/evaluates down to:
${\mathrm{cos}}^{2}\frac{\pi }{8}+{\mathrm{sin}}^{2}\frac{\pi }{8}=1$

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