Question

已知sin(45°+α)=五分之根号五，则sin2α=

要过程，详细！！！感激不尽！！

Answer 1

因：sin(45°+α)=√5/5 sin45°cosa+cos45°sina=√5/5
√2/2xcosa+√2/2xsina=√5/5
√2/2（cosa+sina）=√5/5
cosa+sina=√5/5x2/√2
cosa+sina=2√5/（5√2）=√10/5
两边同时平方得：sin�0�5a+2sinacosa+cos�0�5a=10/25
sin�0�5a+cos�0�5a+2sinacosa=2/5
1+2sinacosa=2/5
1+sin2a=2/5
sin2a=2/5-1
sin2a=-3/5

Answer 2

根号5-根号2