Question

$cos^{2}\frac{\pi }{8} =?$

Answer 1

Ответ:

$\frac{2+\sqrt{2}}{4}$

Answer 2

Используя: $\displaystyle cos(\frac{t}{2} )^2=\frac{1+cos(t)}{2}$

$\displaystyle cos^2(\frac{\pi} {8} )=\frac{1+cos(\frac{\pi }{4} )}{2} =\frac{1+\frac{\sqrt{2} }{2} }{2} =\frac{\frac{2+\sqrt{2} }{2} }{2} =\frac{2+\sqrt{2} }{2} :2=\frac{2+\sqrt{2} }{2} *\frac{1}{2} =\\\\=\frac{(2+\sqrt{2} )*1}{2*2} =\frac{2+\sqrt{2} }{4}$