Question

Найдите значение выражения: $\sqrt{32} cos^{2} \frac{5 \pi }{8} - \sqrt{32} sin^{2} \frac{5 \pi }{8}$

Answer 1

$\sqrt{32}cos^{2} \frac{5\pi}{8} - \sqrt{32}sin^{2} \frac{5\pi}{8} = \sqrt{32}( cos^{2} \frac{5\pi}{8} - sin^{2} \frac{5\pi}{8} )= \sqrt{32}(cos2( \frac{5\pi}{8})=\\ \sqrt{32}(cos \frac{5\pi}{4})= \sqrt{32}(cos(\pi+ \frac{\pi}{4}))=\sqrt{32}(-cos \frac{\pi}{4}) =-\sqrt{32}( \frac{ \sqrt{2} }{2}) =\\ - \sqrt{16} *\sqrt{2} =-4 \sqrt{2}$