Question

Представьте в виде произведение сумму: sinα - sin (α+П/3) ,cos(П/3+α) - cos(П/3-α) ,tg(П/4+α/2) - tg (П/4-α/2)

Answer 1

$sin\alpha-sin(\alpha+\frac{\pi}{3})=2cos(\alpha+\frac{\pi}{6})sin(-\frac{\pi}{6})=-2\cdot \frac{1}{2}cos(\alpha+\frac{\pi}{6})=-cos(\alpha+\frac{\pi}{6})$

$cos(\frac{\pi}{3}+\alpha)-cos(\frac{\pi}{3}-\alpha)=-2sin\frac{\pi}{3}sin\alpha=-2\frac{\sqrt{3}}{2}sin\alpha=-\sqrt{3}sin\alpha$

$tg(\frac{\pi}{4}+\frac{\alpha}{2}))- tg (\frac{\pi}{4}-\frac{\alpha}{2})=\frac{sin\alpha}{cos\frac{\pi}{4}cos\frac{\alpha}{2}}=\frac{\sqrt{2}sin\alpha}{cos\frac{\alpha}{2}}$