已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于（π/4,π/2).(1)求sina和tan2a的值

已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于（π/4,π/2).(1)求sina和tan2a的值
已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于（π/4,π/2).(1)求sina和tan2a的值

已知sina+cosa=3√5/5,a属于(0,π/4),sin(β-π/4)=3/5,β属于（π/4,π/2).(1)求sina和tan2a的值
sina=3√5/5-cosa ,sin^2a=9/5-6√5/5cosa+cos^2a=1-cos^2a ,
4/5-6√5/5cosa+2cos^2a=0 ,(2√5/5-cosa)(√5/5-cosa)=0 ,cosa= 2√5/5
sina=√5/5 ,tana=1/2
tan2a=2tana/(1-tan^2a)=1/(1-1/4)=4/3