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已知向量,,其中A、B是△ABC的内角,⊥,(Ⅰ)求tanAtanB的值;(Ⅱ)求tanC...
试题详情
已知向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALsAAAAkCAYAAADRoEv8AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMIAAAAkCAYAAADb/OWuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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13HSOS9627/76UQQw7sBOEkEtEag6GR1ug4i2PczKEJKnyGc8qGpFDi4mczps1Vb6J9BrbE6gv7b
9+bwBxZOXqvrFaiXcvStQDR5srNhYBiW2vHkOOrB5clpEsMPTHcimLRovTimQk3qSJp0EOeHLKxL
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SoQtpG47iF9VsxhT+3T6AhQ6l73bA0Jgjh8jBpcm5+RsBqRKSeLmRQikmxbEkLqKSs8xpEZlK3OJ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)
,其中A、B是△ABC的内角,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACkSURBVDhP3VO5EQMhDFRdF6icy9UJsQpxSiEE
KmUt2RiOM3OMZxx4LCARu6sHQbi0grQnlAOGrgl+WxK2/dZg5Ib12ZBqmM8jfL+Gk+I6pX8nZHk9
oiBnAUl+63rtkkGZwGoVkCE+ARM8HoRQ7uDwhACj8YfhMwWzOuRgM1+9JlOeqJ8jdjEa03nmThTp
GHxPio7wbcS9O746aUZY/qAR8IPDdwc+xLsdewqvaAAAAABJRU5ErkJggg==
)
⊥
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACySURBVDhPrVO7EYUgEKQuA8oxv06Ir5CXUggB
pezjHsigHKBvZMbAYff2c2owPQFudwgNxswJ6TY4bPunwkw6WD8bXJF5rvB+hsvEtaURwVMJT37q
8qQQ2WKBR0OIYEuYz0dDiAy7Gp/MVoVsx4OORVpGVNIUgtiR0Iel/K4JZoJiR1obEvp2RMGCFU9J
QWnHE8ygANPZEXDN0qf+ZahbloaebHr5M7V7uAMWzP9f612FL960uYg38Ff7AAAAAElFTkSuQmCC
)
,
(Ⅰ)求tanAtanB的值;
(Ⅱ)求tanC的最大值.
相关试题
-
已知向量
,
,其中A、B是△ABC的内角,
⊥
,
(Ⅰ)求tanAtanB的值;
(Ⅱ)求tanC的最大值.
-
设△ABC的三个内角A、B、C对的边分别为a、b、c且a2+b2=mc2(m为常数),若tanC(tanA+tanB)=2tanAtanB,则实数m的值为________.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXZJREFU
WEftVl3OAyEItFf2Ot7Ec3gKL8En7J/4gQv2YZu0m/ShiTDMDCIvaF944kPgJ77wBCiprAMXyLm6
6iopoG38FzNIWRTgCjkGiBJwSZCKXk/NEcJ5oEDCQoQAEZiCW4AIMAXeCu7jSAUTcM2QcpN5SHBy
nAG32BgSHIJsBCJIwg2MmzTkCUp0BYjenV6OQJfHolU7AwZc0p5kqJw5qjIeZKYcSp/0XX34enXl
xcQELBS7KSXn2RiTr13TN1ZBuQagMObdTEmpT7Q8AUHjAEJJXMBKN2s3Yx/TXeftVQqNo95cVGcc
GvRf7uYjzyeOTNe0dB/+QsZyYwivjNhAa+dunkW3ba6AL/TYpQ8e7geGNt0MSX1S43g1bBcG3NnO
9T+8lsL2p+lMv0H3MR6ToeyzBWwC/hYwvreLuD6pGQHmt8VVfmaRMT6fyoZirGEJuKT5W2vBdgNj
JzNfbxZ8rQgXsLzmrknuArZIaD3zA7Yq9fa5P2ekskOeyEPmAAAAAElFTkSuQmCC
)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.
-
已知A,B是△ABC的两个内角,
=
cos![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
+sin![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAXJJREFU
WEftVm2uxCAI9F3Z63gTz8EpvARP6JcYrODbpJv0NdkfmwIzzFD0B+sTnngI+IknPAHKKo+BAXMu
Ll6QAtkmfzGjVmUAXDDHgNEJTCxLjhgS7IQBExE5/199qMCcXBOU+IkCG+E2j1UwAZeMKVeZuwIm
zWtuDAmPfrcGImrCdR1XadgTkuhKUL07vGy6OZQ6fL6zSgBD2tl2zE3dVrpCJa4xnpMTuGcbGslM
wArZTalL+rbOBsy+NkMPCcPgMxiRkNPMRVmBUZ1AoLED4SIu4ME033wZtKWbydtZnktAl0l0Ter0
S0PU1DX6xpVpGqnloBd2rA+GcsqoA7QWNzkWl+0zJb7QY5MubVC7MFzbTSL5pKb1arhdWJpxARcA
cX/y7/TJ1cfCmGNIdv/9iFNdHfeE6LxdxP0DsPDbrNEZuNgxHZ+GI/OGzxIwJP3m6OnbDUyTLHyt
A7biswtYv+auSe4C9kg5i/0Hnin0sfe/Jme7FNKt7l8AAAAASUVORK5CYII=
)
(其中
,
是互相垂直的单位向量),若|
|=
.
(1)试问tanA•tanB是否为定值,若是定值,请求出,否则说明理由;
(2)求tanC的最大值,并判断此时三角形的形状.