Question

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

Answer 1

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