已知sin(2α+β)=3sinβ,tanα=1,求tan(α-β)的值
问题描述:
已知sin(2α+β)=3sinβ,tanα=1,求tan(α-β)的值
答
tanα=1 α=pai/4+k*pai 2α=pai/2+2k*paisin(2α)=1cos(2α)=0sin(2α+β)=sin(2α)cos(β)+cos(2α)sin(β)=3sinβcos(β)=3sinβtan(β)=1/3tan(α-β)=(tan(α)-tan(β))/[1+tan(α)tan(β)]=[1-1/3]/[1+1/3]=1/...