·已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____.

来源：学生作业帮助网编辑：作业帮时间：2024/11/30 10:00:14

x��TMk1�+9f�ɦ��l&�G�V2Ń��V �R�P�"]D�T��^ �Pw�=�S��؞��c�i"{ӛ�0��>��7�|��1W�/?��d��e\D��8{�;z�h\�Y֦�I5{��9Ē��G+/��_��n�o2�v+��}Wt��m�Y�;�g"P�H��p��K��h>d��dX��qW��c�!V��kFAC$��x��x��ʊn�5�{Nuq�VhkA@�!4�z��!��]��w+�A3 �5w��Ջ}��:zV.Ϋ��s��v��š��

·已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____.
·已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____.

·已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____.
tan(a+b)
=2tan[(a+b)/2]/{1-{tan[(a+b)/2]}^2}
=√6/(1-6/4)
=-2√6
tana+tanb
=tan(a+b)*(1-tanatanb)
=-2√6*(1-13/7)
=(12√6)/7
(tana-tanb)^2
=(tana+tanb)^2-4tanatanb
=864/49-52/7
=500/49
tan(a-b)=(tana-tanb)/(1+tanatanb)
[tan(a-b)]^2
=(tana-tanb)^2/(1+tanatanb)^2
=(500/49)/(1+13/7)^2
=5/4
1+[tan(a-b)]^2=1/[cos(a-b)]^2
1+5/4=1/[cos(a-b)]^2
cos(a-b)=2/3
tana和tanb均为正数,tan[(a+b)/2]也为正数且大于1,所以a、b同象限,cos(a-b)为正

tan(a+b) =( 2tan(a+b /2) )/ (1- (tan(a+b /2))^2 )
=√6 / (1-3/2) =-2√6
(tan(a+b))^2 = 24= sec(a+b)^2 -1
sec(a+b)=5 (-5带入后,最后cos(a-b)>1无效)
cos(a+b)=1/5
-----------------
...

全部展开

tan(a+b) =( 2tan(a+b /2) )/ (1- (tan(a+b /2))^2 )
=√6 / (1-3/2) =-2√6
(tan(a+b))^2 = 24= sec(a+b)^2 -1
sec(a+b)=5 (-5带入后,最后cos(a-b)>1无效)
cos(a+b)=1/5
-----------------
cos(a+b)=cosacosb-sinasinb
cosacosb=cos(a+b)+sinasinb=1/5+sinasinb
tanatanb=13/7=sinasinb/cosacosb
sinasinb/(1/5+sinasinb)=13/7
sinasinb=-13/25
cos(a-b)=cos(a+b)+2sinasinb=1/5+2(-13/25)
=-21/25

收起

·已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____. 已知三角形ABC 所对的边分别为a,b,c,tan A +tan B =√3-√3tan A ·tan B.a =2,c =√19.(1)tan已知三角形ABC 所对的边分别为a,b,c,tan A +tan B =√3-√3tan A ·tan B.a =2,c =√19.(1)tan (A +B )值 (2)三角形ABC 面积已知tan(2A-B)=√3(1+M),tan(A-B)-√3[M-tan(2A-B)tan(A-B)],求tanA的值已知tan(a+pai/6)=1/2,tan(b-pai/6)=1/3,则tan(a+b)=? 已知tan(a+b)=3,tan(a-b)=5,求tan 2a,tan 2b的值已知 tan a+b tan b,求 tan a 已知a.b为锐角,tan a ＝1/7,sin b ＝√10/10,求tan （a +2b ）的值, 在三角形ABC中,已知A＋C=2B,求Tan(A/2)+Tan(C/2)＋√3Tan(A/2)×Tan(C/2) 在△ABC中,已知A、B、C成等差数列,求tan(A/2)+tan(C/2)+√3tan(A/2)tan(C/2)的值已知A、B、C成等差数列,求tan（A/2）+tan（C/2)+√3tan(A/2)tan（C/2）的值请写步骤已知A.B.C成等差数列,求tan(A/2)+tan(C/2)+√3tan(A/2)tan(C/2)的值已知tan[(a+b)/2]＝(√6)/2,tanatanb=13/7,求cos(a-b)=____.tan(a+b) =2tan[(a+b)/2]/{1-{tan[(a+b)/2]}^2} =√6/(1-6/4) =-2√6 tana+tanb =tan(a+b)*(1-tanatanb) =-2√6*(1-13/7) =(12√6)/7 (tana-tanb)^2 =(tana+tanb)^2-4tanatanb =864/49-52/7 =500/49 已知tan(a+b)=2tan a 证明 3sinb=sin(2a+b) 已知tan(a-pi/6)=3/7,tan(pi/6+b)=2/5,则tan(a+b)的值已知tan(A-B/2)=2,tan(B-A/2)=-3 求：(1) tan[(A+B)/2] (2) tan(A+B) 已知tan（a+b）=3,tan（a-b)=5,求tan（2a）的值已知tan(a+b)=3,tan(a-b)=5,则tan 2a等于多少? 已知tan(A+B)=2/5,tan(B-π/4)=1/4,求tan(A+π/4已知tan(A+B)=2/5,tan(B-π/4)=1/4,求tan(A+π/4)