已知sin(45度+a)=5/根号5,则sin2a等于多少?老是算错啊

已知sin(45度+a)=5/根号5,则sin2a等于多少?老是算错啊
已知sin(45度+a)=5/根号5,则sin2a等于多少?老是算错啊

已知sin(45度+a)=5/根号5,则sin2a等于多少?老是算错啊
sin(45度+a)
=cos[90度-(45度+a)]
=cos(45度-a)=√5/5
sin2a
=cos(90度-2a)
=cos[2(45度-a)]
=2cos²(45度-a)-1
=2×1/5-1
=-3/5

sin2a = cos (2a -90) = 2*(cos(a-45))^2 - 1
cos(a-45) = cos(45-a) = cos(90-(45+a)) = sin(45+a),
sin2a = 2*(sin(45+a))^2 - 1 = 2 * (根号5 / 5)^2 - 1 = 2 * 1/5 - 1 = - 3/5