已知sina-cosa=2sina*cosa求sin2a的值

已知sina-cosa=2sina*cosa求sin2a的值
已知sina-cosa=2sina*cosa求sin2a的值

已知sina-cosa=2sina*cosa求sin2a的值
两边平方得
1-2sina*cosa = (2sina*cosa)"
(sin2a)" +sin2a-1=0
sin2a = (-1±√5)/2

(sina-cosa)^2=sin^2a+2sinacosa+cos^2a=1+sin2a=(2sinacosa)^2=sin^22a
(sin2a+1/2)^2=5/4
解方程即可

2sina*cosa=sin2a