已知tan(180+α)-tan(450-α)=2（0＜α＜90）求[sec(360+α）-sin(450-α)]/[csc(360-α）-cos(180-α)]的值
问题描述：
已知tan(180+α)-tan(450-α)=2（0＜α＜90）求[sec(360+α）-sin(450-α)]/[csc(360-α）-cos(180-α)]的值
答
∵tan(180°+α)-tan(450°-α)=2 ==>tanα-cotα=2==>sinα/cosα-cosα/sinα=2==>sin²α-cos²α=2sincαosα==>-cos(2α)=sin(2α)==>tan(2α)=-1==>2α=135° (∵0＜α＜90°)==>sin(2α)=1/√2,cos(2...