Question

已知a,b∈(0,π /4),且3sinb=sin(2a+b),4tana/2=1-tan ^ 2a/2,求a+b的值拜

Answer 1

4tana/2=1-tan^2a/2 2tana/2/(1-tan^2a/2)=1/2=tana sina=(1/2)/√(1+1/4)=√5/5 cosa=√(20/25)=2√5/5 sin2a=2*5*2/25=4/5 cos2a=3/5 3sinb=sin2acosb+cos2asinb 15sinb=4cosb+3sinb 12sinb=4cosb tanb=1/3 sinb=(1/3)/√(10/9)=√10/10 cosb=√(1-1/10)=3√10/10 sin(a+b)=sinacosb+cosasinb =3*√5*√10/50+2*√5*√10/50 =5*5√2/50=√2/2 a+b=π/4