Ответ:
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Пошаговое объяснение:
(cos π/8+sin〖π/8〗 )*(〖cos〗^3 π/8-sin^3〖π/8〗 )=〖cos〗^4 π/8-cos π/8*sin^3〖π/8〗+〖cos〗^3 π/8*sin〖π/8〗-sin^4〖π/8〗=
=(〖cos〗^4 π/8-sin^4〖π/8〗 )+(〖cos〗^3 π/8*sin〖π/8〗-cos π/8*sin^3〖π/8〗 )=
(〖cos〗^2 π/8-sin^2〖π/8〗 )(〖cos〗^2 π/8+sin^2〖π/8〗 )+sin〖π/8*〗 cos π/8*(〖cos〗^2 π/8-sin^2〖π/8〗 )=
cos 2π/8*1+1/2*2 sin〖π/8*〗 cos π/8*cos 2π/8=cos π/4*(1+1/2 sin〖2π/8〗 )=cos π/4*(1+1/2 sin〖π/4〗 )=
√2/2*(1+√2/(2*2))=√2/2+〖((√2))/8〗^2=√2/2+1/4