Корень из 32 - корень из 128 sin^2 9pi/8

[latex] \sqrt{32}- \sqrt{128}sin^2 \frac{9 \pi }{8}=\\ \sqrt{32}- 2\sqrt{32}sin^2 \frac{9 \pi }{8}=\\ \sqrt{32}(1- 2sin^2 \frac{9 \pi }{8})=\\\sqrt{32}(sin^2\frac{9 \pi }{8}+cos^2\frac{9 \pi }{8}-2sin^2\frac{9 \pi }{8})=\\\sqrt{32}(cos^2\frac{9 \pi }{8}-sin^2\frac{9 \pi }{8})=\\\sqrt{32}(cos2*\frac{9 \pi }{8})=\\\sqrt{32}(cos \frac{9 \pi }{4})=\\\sqrt{32}* \frac{ \sqrt{2}}{2}=\\ \frac{ \sqrt{64}}{2}= \frac{8}{2}=4[/latex]