4Sinα-3cosα __________ 5sinα Если: а) tgα=2; b) ctgα=3

Question

4Sinα-3cosα
__________
5sinα
Если: а) tgα=2; b) ctgα=3

Answer 1

А) tg(a) = sin(a)/cos(a);
tg(a) = 2; sin(a) = 2cos(a);
cos(a) = x; sin(a) = 2x;
(3*2x - 3x)/(5*2x) = 3x/10x = 3/10.

b) ctg(a) = cos(a)/sin(a);
ctg(a) = 3; cos(a) = 3sin(a);
sin(a) = y; cos(a) = 3y;
(3y - 3*3y)/5y = -6y/5y = -6/5.