tan(π/4+α)+tan(π/4-α)=4,-π

问题描述:

tan(π/4+α)+tan(π/4-α)=4,-π

tan(π/4+α)+tan(π/4-α)=4
即(1+tana)/(1-tana)+(1-tana)/(1+tana)=4,
去分母得(1+tana)^2+(1-tana)^2=4-4(tana)^2,
整理得3(tana)^2=1,
因为a在第三象限,tana=√3/3