sin(a-b)=√10/10,0

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显然cosb>0.sin(a-b)=√10/10得cos(a-b)=±3√10/10.而cosb=cos[a-(a-b)]=cosacos(a-b)+sinasin(a-b)=√5/5*(±3√10/10)+2√5/5*√10/10=(2±3)√50/50显然只能取加号,否则为负值.于是cosb=(2+3)√50/50=√2/2,b=45...
======以下答案可供参考======
供参考答案1:
由sina=2√5/5，cosa=√5/5得出0cosb=cos(a-(a-b))
=cosa*cos(a-b)+sina*sin(a-b)
=√5/5*3√10/10+2√5/5*√10/10
=√2/2 所以b=45度
供参考答案2:
sinacosb-cosasinb=√10/10
(2√5/5)cosb-(√5/5)sinb=√10/10
2cosb-sinb=√2/2
2cosb-√2/2=sinb
4cos(^2)b-2√2cosb+1/2=1-cos(^2)b
3cos(^2)b-2√2cosb-1/2=0
cosb=(2√2+√14)/6