已知a,b属于(0,π/4),且3sinb=sin(2a+b),4tana/2=1-tan62a/2,求a+b的值

问题描述:

已知a,b属于(0,π/4),且3sinb=sin(2a+b),4tana/2=1-tan62a/2,求a+b的值

4tana/2=1-tan^2a/22tana/2/(1-tan^2a/2)=1/2=tanasina=(1/2)/√(1+1/4)=√5/5cosa=√(20/25)=2√5/5sin2a=2*5*2/25=4/5cos2a=3/53sinb=sin2acosb+cos2asinb15sinb=4cosb+3sinb12sinb=4cosbtanb=1/3sinb=(1/3)/√(10...