2个回答
2014-08-10
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(1)由 sin(a/2)+cos(a/2)=6^0.5/2 => (sin(a/2)+cos(a/2))^2=(6^0.5/2 )^2 =>1+sina=3/2
=>sina=1/2 pi/2<=a<=pi => a=pi/6 => cosa=-(3^0.5)/2
(2) sin(a-b)=sinacosb-sinbcosa=-3/5
pi/2<=b<=pi
=> -pi/2<a-b<pi/2 sin(a-b)<0=> -pi<a-b<0
=>cos(a-b)>0 =>cos(a-b)=(1-(sin(a-b))^2)^0.5=4/5
=>cosa*cosb+sinb*sina=4/5 sin(a-b)=sinacosb-sinbcosa=-3/5
cosb=-(3+4*3^0.5)/10
=>sina=1/2 pi/2<=a<=pi => a=pi/6 => cosa=-(3^0.5)/2
(2) sin(a-b)=sinacosb-sinbcosa=-3/5
pi/2<=b<=pi
=> -pi/2<a-b<pi/2 sin(a-b)<0=> -pi<a-b<0
=>cos(a-b)>0 =>cos(a-b)=(1-(sin(a-b))^2)^0.5=4/5
=>cosa*cosb+sinb*sina=4/5 sin(a-b)=sinacosb-sinbcosa=-3/5
cosb=-(3+4*3^0.5)/10
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