Задача 57656 sin(п/6+а...

5f871d864df5f623068f487a

03.02.2021 05:54:09

sin(п/6+а )-cos(п/3+а)/sin(п/6+а)+(п/3+a)

5f3ea7e3faf909182968ddd9

03.02.2021 10:31:10

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Применяем формулы приведения:

[m]cos(\frac{π}{3}+ α )=sin(\frac{π}{2}-(\frac{π}{3}+ α ))=sin(\frac{π}{2}-\frac{π}{3}- α )=sin(\frac{π}{6}- α )[/m]


[m]\frac{sin(\frac{π}{6}+ α )-cos(\frac{π}{3}+ α )}{sin(\frac{π}{6}+ α )+cos(\frac{π}{3}+ α )}=\frac{sin(\frac{π}{6}+ α )-sin(\frac{π}{6}- α )}{sin(\frac{π}{6}+ α )+sin(\frac{π}{6}- α )}=[/m]

По формулам:

[r][m] sin α ± sin β =2sin\frac{ α ± β }{2}\cdot cos\frac{ α \mp β }{2}[/m][/r]