Question

1) 3 корней из 2 sin 9п/8 * cos 9п/8 2) корень из 2 sin 7п/8 * cos 7п/8

Answer 1

$1) 3 \sqrt{2}sin \frac{9 \pi }{8} * cos \frac{9 \pi }{8}= \frac{1}{2}*3 *2\sqrt{2} sin \frac{9 \pi }{8} * cos \frac{9 \pi }{8} =\\ \\ \frac{1}{2}*3 \sqrt{2} sin \frac{2*9 \pi }{8} = \frac{ \sqrt{2} }{2}*sin(2 \pi + \frac{ \pi }{4})= \frac{ \sqrt{2} }{2}* \frac{ \sqrt{2} }{2}=0.5$

$2) \sqrt{2} sin \frac{7 \pi }{8} * cos \frac{7 \pi }{8}= \frac{ \sqrt{2}}{2}*2 sin \frac{7 \pi }{8} * cos \frac{7 \pi }{8}= \frac{ \sqrt{2}}{2}* sin \frac{2*7 \pi }{8} \\ \\ \frac{ \sqrt{2}}{2}* sin \frac{7 \pi }{4}= \frac{ \sqrt{2}}{2} * sin (2 \pi -\frac{ \pi }{4})= - \frac{ \sqrt{2}}{2} * sin \frac{ \pi }{4}=- \frac{ \sqrt{2}}{2} * \frac{ \sqrt{2}}{2} =0.5$