诱导公式计算已知tan(π+α)=2,求sin²(π-α)-sin(0.5π+2)×cos(0.5π-2)+2=?等明天老师讲明白了，我把正确的发上来

Question

诱导公式计算
已知tan(π+α)=2,求sin²(π-α)-sin(0.5π+2)×cos(0.5π-2)+2=?
等明天老师讲明白了，我把正确的发上来

Answer 1

sin²(π-α)-sin(0.5π+2)×cos(0.5π-2)+2
=sin²(α)-cos2sin2+2
=(14/5)-cos2sin2
tan(π+α)=2=tanα ,2cosα=sinα ,
4cos^2(α)=sin^2(α) ,4-4sin^2(α)=sin^2(α)
sin^2(α)=4/5