已知:5sinα=3sin(α-2β),(β≠kπ+π/2,k∈Z),求证:tan(α-β)+4tanβ=0
问题描述:
已知:5sinα=3sin(α-2β),(β≠kπ+π/2,k∈Z),求证:tan(α-β)+4tanβ=0
答
5sina=5sin(a-b+b)=5sin(a-b)cosb+5cos(a-b)sinb=3sin(a-2b)=3sin(a-b)cosb-3sin(a-b)cosb; 4cos(a-b)sinb=-sin(a-b)cosb;tan(α-β)+4tanβ=0