A B C分别是a b c的对边若a,b,c,成等比数列,且cosB=3/5,求cosA/sinA+cosC/sinc的
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A B C分别是a b c的对边若a,b,c,成等比数列,且cosB=3/5,求cosA/sinA+cosC/sinc的
A B C分别是a b c的对边若a,b,c,成等比数列,且cosB=3/5,求cosA/sinA+cosC/sinc的
A B C分别是a b c的对边若a,b,c,成等比数列,且cosB=3/5,求cosA/sinA+cosC/sinc的
a,b,c成等比数列,所以a*c=b^2
根据正弦定理,a/sinA=b/sinB=c/sinC
所以sinA=a/b*sinB,sinC=c/b*sinC
有cosB=3/5
sinB=根号1-9/25=4/5
cosA/sinA+cosC/sinc
=(cosA*sinC+sinA*cosC)/sinA*sinC
=sin(A+C)/[(a/b*sinB)*(c/b*sinB)]
=sinB/[(a/b*sinB)*(c/b*sinB)]
=1/sinB
=5/4
cosB=3/5 得 cosA cosC-sinA sinC=cos(A+C)=-3/5
sinB=4/5 得 sinA cosC+cosA sinC=4/5
bb=ac 得 sinA sinC=sinB sinB=16/25
所以 cosA cosC=1/25
tanA+tanC=(sinA cosC+cosA sinC)/(cosA cosC)=20继续求 ...
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cosB=3/5 得 cosA cosC-sinA sinC=cos(A+C)=-3/5
sinB=4/5 得 sinA cosC+cosA sinC=4/5
bb=ac 得 sinA sinC=sinB sinB=16/25
所以 cosA cosC=1/25
tanA+tanC=(sinA cosC+cosA sinC)/(cosA cosC)=20
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a、b、c成等比数列,所以a*c=b^2;
根据正弦定理a/sinA=b/sinB=c/sinC得sinA=(a/b)*sinB,sinC=(c/b)*sinC;
cosA/sinA+cosC/sinC
=(cosA*sinC+sinA*cosC)/sinA*sinC
=sin(A+C)/[(a/b)*sinB*(c/b)*sinB]
=sin(180°...
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a、b、c成等比数列,所以a*c=b^2;
根据正弦定理a/sinA=b/sinB=c/sinC得sinA=(a/b)*sinB,sinC=(c/b)*sinC;
cosA/sinA+cosC/sinC
=(cosA*sinC+sinA*cosC)/sinA*sinC
=sin(A+C)/[(a/b)*sinB*(c/b)*sinB]
=sin(180°-B)/[(ac/b^2)sinB*sinB]
=1/sinB
又cosB=3/5,由平方关系得sinB=根号1-9/25=4/5,故cosA/sinA+cosC/sinC=5/4
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