3tan(a-π/12)=tan(a+π/12) 求a
问题描述：
3tan(a-π/12)=tan(a+π/12) 求a
答
3tan(a-π/12)=tan(a+π/12)
3sin(a-π/12)cos(a+π/12)=sin(a+π/12)cos(a-π/12)
3[sin2a-sin(π/6)]=sin2a+sin(π/6)
2sin2a=4sin(π/6)=4*(1/2)=2
sin2a=1
2a=2kπ+π/2
a=kπ+π/4 (k∈Z)