已知tan(π/12+A)=根号2,tan(B-π/3)=2根号2,求tan(A+B)的值

问题描述:

已知tan(π/12+A)=根号2,tan(B-π/3)=2根号2,求tan(A+B)的值

π/12+A+B-π/3=A+B-π/4,
tan(A+B-π/4)=(√2+2√2)/[1-√2*2√2]=-√2,
∴tan(A+B)=(1-√2)/(1+√2)=-3+2√2.