在△ABC中,A、B、C为三内角,tan C=-(cos A-cos B)/(sin A-sin B),sin(B-A)=cos C,求A、C的值.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 14:28:58
![在△ABC中,A、B、C为三内角,tan C=-(cos A-cos B)/(sin A-sin B),sin(B-A)=cos C,求A、C的值.](/uploads/image/z/6888062-38-2.jpg?t=%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2CA%E3%80%81B%E3%80%81C%E4%B8%BA%E4%B8%89%E5%86%85%E8%A7%92%2Ctan+C%3D-%28cos+A-cos+B%29%2F%28sin+A-sin+B%29%2Csin%28B-A%29%3Dcos+C%2C%E6%B1%82A%E3%80%81C%E7%9A%84%E5%80%BC.)
xRMK@+A1MkkL`wI%RKC$~*ɯMZOlh詇ly2ot4BNg?{G8'v5 hܢS×.,n u%_JNY/pw|z
32OB@
@4Mq*tb+&2:dI`
I@pQ--Qfwq$N2͓0ﴦ.
фLuɊ֦][_sڭm5*KjYh(=
-^4.qi C%YV\fsa
S1wdt;G7DZ0
在△ABC中,A、B、C为三内角,tan C=-(cos A-cos B)/(sin A-sin B),sin(B-A)=cos C,求A、C的值.
在△ABC中,A、B、C为三内角,tan C=-(cos A-cos B)/(sin A-sin B),sin(B-A)=cos C,求A、C的值.
在△ABC中,A、B、C为三内角,tan C=-(cos A-cos B)/(sin A-sin B),sin(B-A)=cos C,求A、C的值.
tan C=-(cos A-cos B)/(sin A-sin B)
sinC/cosC=-(cos A-cos B)/(sin A-sin B)
sinAsinC-sinBsinC=cosBcosC-cosAcosC
sinAsinC+cosAcosC=cosBcosC+sinBsinC
cos(A-C)=cos(B-C)
∴A-C=B-C,或 A-C=C-B
若A-C=B-C,==>A=B 不符合题意(分母为0)
∴A-C=C-B==>A+B=2C,
A+B+C=180º ,3C=180º,C=60º
sin(B-A)=cos C=1/2
∴B-A=30º (∵-120º≤B-A≤120º)
B-A=30º ,B+A=120º ,∴B=75º,A=45º
∴A=45º,C=60º
,