Ответ:

sin(a + b) = sin a cos b + cos a sin b

sin(π/6) = 1/2, cos(π/6) = √3/2

Тоді маємо:

2 sin(a + π/6) - cos a

= 2(sin a cos(π/6) + cos a sin(π/6)) - cos a (using the identity sin(a + b))

= sin a √3 + cos a - cos a

= sin a √3

Тому спрощеним виразом є:

2 sin(a + π/6) - cos a = sin a √3

[tex]\displaystyle\bf\\2Sin\Big(\alpha +\frac{\pi }{6}\Big)-Cos\alpha =2\cdot \Big(Sin\alpha Cos\frac{\pi }{6} +Sin\frac{\pi }{6} Cos\alpha \Big)-Cos\alpha =\\\\\\=2\cdot\Big(Sin\alpha \Cdot \frac{\sqrt{3} }{2} +\frac{1}{2} Cos\alpha\Big)-Cos\alpha = \sqrt{3} Sin\alpha +Cos\alpha -Cos\alpha =\\\\\\=\sqrt{3} Sin\alpha[/tex]