sina+cosa=√2sina,则sin2a=?

sina+cosa=√2sina,则sin2a=?
sina+cosa=√2sina,则sin2a=?

sina+cosa=√2sina,则sin2a=?
cosa=(√2-1)sina,sina^2+cosa^2=1
sina^2+((√2-1)sina)^2=1
(1+3-2√2)(sina^2)=1
sina^2=(2+√2)/4
sin2a=2sinacosa=2(√2-1)sina^2=2(√2-1)(2+√2)/4=√2/2

sina+cosa=√2sina
sin^2a+2sinacosa+cos^2a=2sin^2a
sin2a=sin^2a-cos^2a
sin2a=-cos2a
tan2a=-1
2a=135或2a=315
则sin2a=√2/2 或sin2a=-√2/2

sina+cosa=√2sina
两边同除以cosa得
tana+1=√2tana
tana=1/(√2-1)=√2+1
sin2a
=2tana/(1+tan^2a)
=(2√2+2)/(1+(√2+1)^2)
=(√2+1)/(2+√2)
=(√2+1)*(2-√2)/2
=√2/2