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

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

$cos(frac{pi}{3}+alpha)-cos(frac{pi}{3}-alpha)=-2sinfrac{pi}{3}sinalpha=-2frac{sqrt{3}}{2}sinalpha=-sqrt{3}sinalpha$

$tg(frac{pi}{4}+frac{alpha}{2}))- tg (frac{pi}{4}-frac{alpha}{2})=frac{sinalpha}{cosfrac{pi}{4}cosfrac{alpha}{2}}=frac{sqrt{2}sinalpha}{cosfrac{alpha}{2}}$