已知sina-cosa=1/5,且a属于(0,π/2) (1)求sina和cosa的值 （2）求cos（2a-π/4)的值

已知sina-cosa=1/5,且a属于(0,π/2) (1)求sina和cosa的值 （2）求cos（2a-π/4)的值

（1）（sina+cosa)^2+(sina-cosa)^2=2
因为a属于(0,π/2)
所以sina+cosa>0
sina+cosa=7/5
因为sina+cosa=1/5
所以sina=4/5
cosa=3/5
（2）sin2a=2sinacosa=24/25
cos2a=2cos^2a-1=-7/25
cos（2a-π/4)
=cos2a*cosπ/4+sin2a*sinπ/4
=根号2/2（sin2a+cos2a)
=根号2/2*17/25
=17根号2/50

sina sina + cosa cosa = 1 (sina-cosa)^2 =1/25= sina sina + cosa cosa -2sina cosa=1-sin2a sin2a=24/25, 因为，0≤a≤π，sin2a>0 0≤2a≤π 0≤a≤π/2 (cosa + sina )^2= sina sina + cosa cosa + 2sina cosa=1+24/25=(7/5)^2 cosa + sina=7/5 cos2a=cosa cosa - sina sina=(cosa - sina )(cosa + sina )=-7/25 sin(2a-π/4)=sin2a cos(π/4)-sin(π/4) cos2a =(24/25+7/25)*√2/2 =(16√2) /25