Question

1)cosa*cos3a-sina*sin3a 2) sin2a*cosa+cos2a*sina 3) sin40*cos5+cos40*sin5 4) (tg7П/15-tg2П/15)/1+tg7П/15*tg2П/15 5) sina=4/5;П<a<3П/2; cosa-?

Answer 1

1)cosa*cos3a-sina*sin3a =cos(a+3a)=cos4a
2) sin2a*cosa+cos2a*sina = sin(2a+a)=sin3a
3) sin40*cos5+cos40*sin5 =sin(40+5)=sin45=√2/2
4) (tg7П/15-tg2П/15)/1+tg7П/15*tg2П/15=tg(7П/15-2П/15)=tg(п/3)=√3
5) sina=-4/5;П<a<3П/2; cosa-?
cosa на отрезке П<a<3П/2 отрицателен.
1-sin^2a=cos^2a=1-16/25=9/25
cosa=-3/5