Question

Преобразуйте выражение sin(pi/3+x)-sinx

Answer 1

$\sin\Big(\dfrac{\pi}3+x\Big)-\sin x=\\\\=2\cdot\sin\Big(\dfrac{\frac{\pi}3+x-x}2\Big)\cdot\cos\Big(\dfrac{\frac{\pi}3+x+x}2\Big)=\\\\=2\cdot\sin\Big(\dfrac{\pi}6\Big)\cdot \cos\Big(\dfrac{\pi}6+x\Big)=\\\\=2\cdot\dfrac 12\cdot \cos\Big(\dfrac{\pi}6+x\Big)\boldsymbol{=\cos\Big(\dfrac{\pi}6+x\Big)}$