Question

已知sin(a-45°)=根号5/5,则sina2a=?

已知sin(a-45°)=根号5/5,则sina2a=? 拜托详细点解答

Answer 1

解：因为 cos（ a+45度）=cos[90度+（a--45度）]=sin(a--45度）=根号5/5，
所以 sin(a+45度）=（2根号5）/5，cos(a--45度）=（2根号5）/5，
所以 sin2a=sin[(a+45度)+(a--45度)]
=sin(a+45度）cos(a--45度)+cos(a+45度)sin(a--45度)
=[（2根号5）/5]*[（2根号5）/2]+[（根号5）/5]*[（根号5）/5]
=20/25+5/25
=1。

Answer 2

sin(a-45°)=sinacos45°-cosasin45°=(sina-cosa)*√2/2=√5/5
=>sina-cosa=√10/5
=>(sina-cosa)^2=(sina)^2+(cosa)^2-2sinacosa=1-sin2a=2/5
=>sin2a=3/5

Answer 3

sin(a-45°)
=sin(a)cos(45°)-sin(45°)cos(a)
=(√2/2) * (sina-cosa)
=√5/5

sina-cosa=√(2/5)

(sina-cosa)²
=sin²a-2sinacosa+cos²a
=1-sin2a
=2/5

sin2a=1-2/5=3/5