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