sin + sin

[Гост]

sin70* + sin50* =?

представете като произведение

[Добромир Глухаров]

Ами по формулата: [tex]sin\alpha+sin\beta=2sin{\frac{\alpha+\beta}{2}}cos{\frac{\alpha-\beta}{2}}[/tex]

[tex]sin70^\circ+sin50^\circ=2sin\frac{70^\circ+50^\circ}{2}cos\frac{70^\circ-50^\circ}{2}=2sin60^\circ cos10^\circ=\sqrt{3}cos10^\circ[/tex]

[Гост]

Благодаря. Ами sin[tex]\pi[/tex]/6 - sin\pi/9

[Добромир Глухаров]

[tex]sin\alpha-sin\beta=2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2}[/tex]

[tex]sin\frac{\pi}{6}-sin\frac{\pi}{9}=2sin\frac{\frac{\pi}{6}-\frac{\pi}{9}}{2}cos\frac{\frac{\pi}{6}+\frac{\pi}{9}}{2}=2sin\frac{\frac{3\pi}{18}-\frac{2\pi}{18}}{2}cos\frac{\frac{3\pi}{18}+\frac{2\pi}{18}}{2}=2sin\frac{\frac{\pi}{18}}{2}cos\frac{\frac{5\pi}{18}}{2}=2sin{\frac{\pi}{36}}cos{\frac{5\pi}{36}}[/tex]