Question

Доказать, что:
$sin(10) times sin(50) times sin(70) = frac{1}{8}$

Answer 1

sin10*sin50*sin70*cos10/cos10=sin20*sin50*sin(90-20)/(2cos10)=
=sin20sin50cos20/(2cos10)=sin40*sin50/(4cos10)=sin40*sin(90-40)/(4cos10)=
=sin40cos40/(4cos10)=sin80/(8cos10)=sin(90-10)/(8cos10)=cos10/(8cos10)=
=1/8

Answer 2

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