Question

已知 tan a =1 3sin(a+b)=sin(2a+b) ,求 tan(a+b) 的 值.

Answer 1

tana=1

cosa=√2/2,sina=√2/2 或 cosa=-√2/2,sina=-√2/2

cos2a=0,sin2a=1 cos2a=0,sin2a=1

3sin(a+b)=sin(2a+b)

(3√2/2)(sinb+cosb)=cosb

3√2sinb=(2-3√2)cosb

tanb=(2-3√2)/3√2=√2/3-1

tan(a+b)=(tana+tanb)/(1-tanatanb)=(√2/3)/(1-(√2/3-1))=√2/(6-√2)