Question

已知sina+cosa/sina-cosa =2则sinacosa的值

Answer 1

sina+cosa/sina-cosa =2

同时除以cosa

(1+tana)/(tana-1)=2

(1+tana)/(1-tana)=-2

(tan45+tana)/(1-tan45*tana)=-2

tan(45+a)=-2

tan(90+2a)=2*tan(45+a)/(1-tan(45-a)^2)

tan(90+2a)=4/3

cot2a=-4/3

sin2a=3/5 或 sin2a=-3/5

sinacosa=1/2*sin2a=3/10 或 sin2a=-3/10