Question

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

Answer 1

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

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

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

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

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

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

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

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