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已知cosa=1/7,cos(a-b)=13/14,且0＜b＜a＜派/2.求b
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已知cosa=1/7,cos(a-b)=13/14,且0＜b＜a＜派/2.求b
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0＜b＜a＜π/2
0＜a-b＜π/2
cosa=1/7,sina=√(1-(1/7)^2)=4√3/7
cos(a-b)=13/14,sin(a0b)=√(1-(13/14)^2)=3√3/14
sinb=sin[a-(a-b)]
= sinacos(a-b)-cosasin(a-b)
= 4√3/7*13/14-1/7*3√3/14
= (52√3-3√3)/98
= √3/2
b=60°
0＜a-b＜π/2
cosa=1/7,sina=√(1-(1/7)^2)=4√3/7
cos(a-b)=13/14,sin(a0b)=√(1-(13/14)^2)=3√3/14
sinb=sin[a-(a-b)]
= sinacos(a-b)-cosasin(a-b)
= 4√3/7*13/14-1/7*3√3/14
= (52√3-3√3)/98
= √3/2
b=60°
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