Question

-cosπ/7*cos3π/7*cos2π/7
помогите пожалуйста

Answer 1

-cosπ/7*cos3π/7*cos2π/7
$-cos frac{ pi }{7} *cos frac{2 pi }{7} *cos frac{3 pi }{7} = \ \ =- frac{2sin frac{ pi }{7}*cos frac{ pi }{7} }{2sin frac{ pi }{7} } *cos frac{2 pi }{7} *cos frac{3 pi }{7}= \ \ =- frac{sin frac{2 pi }{7} }{2sin frac{ pi }{7} } *cos frac{2 pi }{7} *cos frac{3 pi }{7} = \ \ =- frac{2sin frac{2 pi }{7}*cos frac{2 pi }{7} }{4sin frac{ pi }{7} } *cos frac{3 pi }{7} =$
$=- frac{sin frac{4 pi }{7} }{4sin frac{ pi }{7} } *cos( pi - frac{ 4pi }{7} )= frac{sin frac{4 pi }{7} }{4sin frac{ pi }{7} } *cos frac{ 4pi }{7} = \ \ = frac{2sin frac{4 pi }{7} *cos frac{ 4pi }{7}}{8sin frac{ pi }{7} } = frac{sin frac{8 pi }{7} }{8sin frac{ pi }{7} } = frac{sin( pi + frac{ pi }{7} )}{8sin frac{ pi }{7} } = \ \ =- frac{sin frac{ pi }{7} }{8sin frac{ pi }{7} } =- frac{1}{8} =-0,125$