Question

тригонометрия. найдите значения выражений

Answer 1

Всё решаем по формулам.

Answer 2

$sqrt{32}- sqrt{128}Sin^2 frac{9 pi }{8}=4 sqrt{2}-8 sqrt{2}Sin^2( pi + frac{ pi }{8})=4 sqrt{2}-8 sqrt{2}Sin^2 frac{ pi }{8}=$

$=4 sqrt{2}-8 sqrt{2}* frac{1}{2}(1-Cos frac{ pi }{4})=4 sqrt{2}-4 sqrt{2}(1- frac{ sqrt{2}}{2})=4$

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$sqrt{128}*Cos^2 frac{7 pi }{8}- sqrt{32}=8 sqrt{2}*Cos^2( pi - frac{ pi }{8})-4 sqrt{2}=$

$=8 sqrt{2}Cos^2 frac{ pi }{8}-4 sqrt{2}=8 sqrt{2}* frac{1}{2}(1+Cos frac{ pi }{4})-4 sqrt{2}=4 sqrt{2}+4-4 sqrt{2}=4$

*******

$6 sqrt{2}Cos frac{ pi }{4}Cos frac{7 pi }{3}=6 sqrt{2}* frac{ sqrt{2} }{2}*Cos(2 pi + frac{ pi }{3})=6Cos frac{ pi }{3}=6* frac{1}{2}=3$