Тригонометрия - да се опрости sin10 * sin50 * sin70

[tbgspitfire]

[tex]sin10^\circ sin50^\circ sin70^\circ[/tex]

[strangerforever]

[tex]sin10^\circ sin50^\circ sin70^\circ = sin10^\circ sin50^\circ cos20 = \frac{2sin10^\circ sin50^\circ cos20^\circ cos10^\circ }{2cos10^\circ } = \frac{sin20^\circ sin50^\circ cos20^\circ }{2cos10^\circ }[/tex]

[tex]= \frac{sin40^\circ sin50^\circ }{4cos10^\circ } = \frac{sin40^\circ cos40^\circ }{4cos10^\circ } = \frac{sin80^\circ }{8cos10^\circ } = \frac{cos10^\circ }{8cos10^\circ } = \frac{1}{8}[/tex]

[tex]sin3x=4sin(60^\circ -x)sinxsin(60^\circ +x)=>sin(60^\circ -x)sinxsin(60^\circ +x)=\frac{1}{4 } sin3x[/tex]

[tex]sin50^\circ sin10^\circ sin70^\circ =sin(60^\circ -10^\circ )sin10^\circ sin(60^\circ +10^\circ )=\frac{1}{ 4} sin30^\circ =\frac{1}{8 }[/tex]

[tbgspitfire]

Много благодаря! Вече знам как се решават.