sin(a-b)=√10/10,0

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sin(a-b)=√10/10,0
sin(a-b)=√10/10,0

sin(a-b)=√10/10,0
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°.

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

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

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