已知sin(π/4—a)=5/13,0＜a＜π/4,则cos2a等于多少?

已知sin(π/4—a)=5/13,0＜a＜π/4,则cos2a等于多少?
已知sin(π/4—a)=5/13,0＜a＜π/4,则cos2a等于多少?

已知sin(π/4—a)=5/13,0＜a＜π/4,则cos2a等于多少?
因为0＜a＜π/4
所以0＜π/4-a＜π/4
cos(π/4-a)>0
cos(π/4-a)=√[1-(5/13)^2]=12/13
cos2a=sin(π/2-2a)
=sin2(π/4-a)
=2sin(π/4-a)cos(π/4-a)
=2*(5/13)*(12/13)
=120/169