Question

вычислите sin π/8 * cos³ π/8 * sin³ π/8

Answer 1

$sin \frac{\pi}{8} \cdot cos^3 \frac{\pi}{8} \cdot sin^3 \frac{\pi}{8}=$

$\sqrt{ \frac{1-cos \frac{\pi}{4} }{2} } \cdot (cos \frac{\pi}{8} \cdot sin \frac{\pi}{8})^3=$

$\sqrt{ \frac{1- \frac{ \sqrt{2} }{2} }{2} } \cdot ( \frac{1}{2} \cdot 2 cos \frac{\pi}{8} \cdot sin \frac{\pi}{8})^3=$

$\sqrt{ \frac{2- \sqrt{2} }{4} } \cdot \frac{1}{8} \cdot (2 cos \frac{\pi}{8} \cdot sin \frac{\pi}{8})^3=$

$\frac{ \sqrt{2- \sqrt{2} } }{2} \cdot \frac{1}{8} \cdot (sin \frac{\pi}{4})^3=$

$\frac{\sqrt{2- \sqrt{2} }}{16} \cdot \left( \frac{ \sqrt{2} }{2} \right) ^3=$

$\frac{\sqrt{2- \sqrt{2} }}{16} \cdot \frac{ \sqrt{2} }{4}=$

$\frac{\sqrt{4-2 \sqrt{2} }}{64}$