Question

1. ВЫЧИСЛИТЬ cosП/7+соs6П/7+sinП/5-sin4П/5
2.УПРОСТИТЬ
sin2a/1-cos2a*1-cosa/cosa

Answer 1

Формулы для первого примера на фото.

$...=2cosbigg( dfrac{ pi +6 pi }{2cdot 7} bigg)cosbigg( dfrac{ pi-6 pi }{2cdot7} bigg)+2cosbigg( dfrac{ pi +4 pi }{2cdot5} bigg)sinbigg( dfrac{ pi-4 pi }{5cdot 2} bigg)=\ \ \ =2cosbigg( dfrac{ pi }{2} bigg)cosbigg(- dfrac{ 5pi }{14} bigg)+2cosbigg( dfrac{ pi }{2} bigg)sinbigg(- dfrac{3 pi }{10} bigg)=0+0=0$


$displaystyle frac{sin2 alpha }{1-cos2 alpha } cdot frac{1-cos alpha }{cos alpha } = frac{sin2 alpha }{1-1+2sin^2 alpha } cdot frac{1-cos alpha }{cos alpha } =\\\= frac{sin2 alpha }{2(1-cos^2 alpha )} cdot frac{1-cos alpha }{cos alpha } = frac{2sin alpha cos alpha }{2(1-cos alpha )(1+cos alpha )} cdot frac{1-cos alpha }{cos alpha } =\\\= frac{sin alpha }{1+cos alpha } .$