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在△ABC中,若sin2A+sin2B=5sin2C,则cosC的最小值等于A.B.C.D...
试题详情
在△ABC中,若sin
2A+sin
2B=5sin
2C,则cosC的最小值等于( )
A.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALdJREFU
OE+9U9EVhDAI663MOmzCHEzRJZCW6ysoracfh8+fvhjSJH5Ep+ymAXZTHgKqEBRBnp8FhkrQ9CwA
lQSJVwxKjSRVn3QFIwjVtjcDMLqdCYCxdGHnF4xSTj7cXDPXEKy8Zbga/zSLNwyZB+Ms8eHNip8b
NcrS90OL3ubrAwu6Q89qgBB5XKoA89+uhuL6eo3bujHaFTRM2i7W9T4JKwrOATuG2fChQX8YcKX1
v92/w1qlegCBfNWPn8LVvwAAAABJRU5ErkJggg==
)
B.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAANtJREFU
SEvNVcENwyAMpCt7HW/iOZiCJVzAQhiSFGykto7yQeJydz47L84VTqoAnFQ4uVzZ2wASEwTG2G+Z
ABJB8csJkIiRopdBpo7EKT8uCRGBKRXdHoCISrMDIGKoxs0vCKUvt9HnwZA0hwerpJqSeAd2DvDU
pto2PTUPWpYM7jLQzhw5uNJYMvifLrRlUvVDGW2pTQmRUV3SsvYAhpEeXdkAkPxL65DVPrVIkK9K
6Np2MnnQaVczVUI3JMxJGA31AZww6Bt614P8QwG1VOcBdUgw5+DzOP2ewRtSqfyBrZ/HUAAAAABJ
RU5ErkJggg==
)
C.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAMhJREFU
OE+9ktERxCAIRLmWbYdOrIMqbIIDDQbUY/KROWfykWRZnrAflgPZUUF24JmAUNuMp1Rurgq4VS5I
1ydiVNF8F75GFCpaLcFlZ9B23mGFJAR2/zk6BJ5R6gSNa0E2XHOeAsLC1d/vUnSBkvu+LKD2Dgo1
h2TDgrvVw1EnC3nBYQe8oZdBnUFeYDDjnoNDqq4WkqQlanFZbvYrqjjomu1qybq1ciwurn27ZofN
Mik+AfgwKBHkqV4ZNMkzSTHy/17Wr1h+ATWw10memLcaAAAAAElFTkSuQmCC
)
D.
相关试题
-
在△ABC中,若sin2A+sin2B=5sin2C,则cosC的最小值等于( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALdJREFU
OE+9U9EVhDAI663MOmzCHEzRJZCW6ysoracfh8+fvhjSJH5Ep+ymAXZTHgKqEBRBnp8FhkrQ9CwA
lQSJVwxKjSRVn3QFIwjVtjcDMLqdCYCxdGHnF4xSTj7cXDPXEKy8Zbga/zSLNwyZB+Ms8eHNip8b
NcrS90OL3ubrAwu6Q89qgBB5XKoA89+uhuL6eo3bujHaFTRM2i7W9T4JKwrOATuG2fChQX8YcKX1
v92/w1qlegCBfNWPn8LVvwAAAABJRU5ErkJggg==
)
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAANtJREFU
SEvNVcENwyAMpCt7HW/iOZiCJVzAQhiSFGykto7yQeJydz47L84VTqoAnFQ4uVzZ2wASEwTG2G+Z
ABJB8csJkIiRopdBpo7EKT8uCRGBKRXdHoCISrMDIGKoxs0vCKUvt9HnwZA0hwerpJqSeAd2DvDU
pto2PTUPWpYM7jLQzhw5uNJYMvifLrRlUvVDGW2pTQmRUV3SsvYAhpEeXdkAkPxL65DVPrVIkK9K
6Np2MnnQaVczVUI3JMxJGA31AZww6Bt614P8QwG1VOcBdUgw5+DzOP2ewRtSqfyBrZ/HUAAAAABJ
RU5ErkJggg==
)
C.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAMhJREFU
OE+9ktERxCAIRLmWbYdOrIMqbIIDDQbUY/KROWfykWRZnrAflgPZUUF24JmAUNuMp1Rurgq4VS5I
1ydiVNF8F75GFCpaLcFlZ9B23mGFJAR2/zk6BJ5R6gSNa0E2XHOeAsLC1d/vUnSBkvu+LKD2Dgo1
h2TDgrvVw1EnC3nBYQe8oZdBnUFeYDDjnoNDqq4WkqQlanFZbvYrqjjomu1qybq1ciwurn27ZofN
Mik+AfgwKBHkqV4ZNMkzSTHy/17Wr1h+ATWw10memLcaAAAAAElFTkSuQmCC
)
D.
-
在△ABC中,若sin2A+sin2B=5sin2C,则cosC的最小值等于( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALdJREFU
OE+9U9EVhDAI663MOmzCHEzRJZCW6ysoracfh8+fvhjSJH5Ep+ymAXZTHgKqEBRBnp8FhkrQ9CwA
lQSJVwxKjSRVn3QFIwjVtjcDMLqdCYCxdGHnF4xSTj7cXDPXEKy8Zbga/zSLNwyZB+Ms8eHNip8b
NcrS90OL3ubrAwu6Q89qgBB5XKoA89+uhuL6eo3bujHaFTRM2i7W9T4JKwrOATuG2fChQX8YcKX1
v92/w1qlegCBfNWPn8LVvwAAAABJRU5ErkJggg==
)
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAANtJREFU
SEvNVcENwyAMpCt7HW/iOZiCJVzAQhiSFGykto7yQeJydz47L84VTqoAnFQ4uVzZ2wASEwTG2G+Z
ABJB8csJkIiRopdBpo7EKT8uCRGBKRXdHoCISrMDIGKoxs0vCKUvt9HnwZA0hwerpJqSeAd2DvDU
pto2PTUPWpYM7jLQzhw5uNJYMvifLrRlUvVDGW2pTQmRUV3SsvYAhpEeXdkAkPxL65DVPrVIkK9K
6Np2MnnQaVczVUI3JMxJGA31AZww6Bt614P8QwG1VOcBdUgw5+DzOP2ewRtSqfyBrZ/HUAAAAABJ
RU5ErkJggg==
)
C.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAMhJREFU
OE+9ktERxCAIRLmWbYdOrIMqbIIDDQbUY/KROWfykWRZnrAflgPZUUF24JmAUNuMp1Rurgq4VS5I
1ydiVNF8F75GFCpaLcFlZ9B23mGFJAR2/zk6BJ5R6gSNa0E2XHOeAsLC1d/vUnSBkvu+LKD2Dgo1
h2TDgrvVw1EnC3nBYQe8oZdBnUFeYDDjnoNDqq4WkqQlanFZbvYrqjjomu1qybq1ciwurn27ZofN
Mik+AfgwKBHkqV4ZNMkzSTHy/17Wr1h+ATWw10memLcaAAAAAElFTkSuQmCC
)
D.
-
在△ABC中,sin2A+sin2B=5sin2C,则角C的范围是________.
-
已知cosB=cosθ•sinA,cosC=sinθsinA.求证:sin2A+sin2B+sin2C=2.
-
在△ABC中,已知sin2A=sin2B+sinBsinC+sin2C,则A等于( )
A.30°
B.60°
C.120°
D.150°
-
在△ABC中,sin2A=sin2B+sin2C-
sinBsinC,且![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAATCAYAAACUef2IAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAONJREFU
OE/tVNENxCAI5VZ2HTZhDqdwCQ5Bq1B6aXJ3f21ik1p4vvdAXgDAsn76MAukvP7yPMCHrR+sqEzU
nP8VtdB+FWIfZSkXwI2pAJcA3BMaFQas48DK2A86vhePFFiTJeEcbwfu+6riFnAjRhIbAoBykX8F
kCdfI1A4ERatEGnqWZd4TphKps+ZVdMMZ0XFwSYws+Bgg8bkdXDFi2xgk5zZ0PesS5Y1ewsZY/V1
a5qKDKGNfDcsBTFuWdElZSBu76Ib0s4ZfWyFmIUygHUJRGZnHy+Fy8ln2DOE7gyh7+b/G1mGnIzq
VOu/AAAAAElFTkSuQmCC
)
=2
,则AC+2AB的 最小值为( )
A.4![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAASCAYAAACEnoQPAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALtJREFU
OE/Nk9sVhCAMRENH9EMXFEET9EAB1ME59pAmsgmPFRF15Wv5UuQymUlUxAuGpZQat+bvAo+LT862
z+f+HMZIlq2IHfDpW+zU3NFzIm8jYUb4mS9o/DOMWMEimPwbuE80+bdl74oLnjvpGpyNJYFnz8Mg
YLQENUCgYEoLwOwtuJuwzjeEEDLkNJB2WynnEkaKdpZ2rqCoH2BRagPS9fjk2fBHUV/6MTanCbRb
g6UUUV9SbnH/Cn8A/r2EUaEPy7EAAAAASUVORK5CYII=
)
B.4![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAASCAYAAACEnoQPAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAMZJREFU
OE/VU9sNhSAMLRuxD1swBEuwAwMwB4k7sERvSysKmkj4u/1C7Ol5WA1SwVTGmPnq/ZnBc1Hn2/Wz
70/ANaMnSwAec6WsVmXX7DvoxKyBSyRgxDIxLYArZg8YIw9gyXTWKd9gZY1FEHf5n+DW7DNSPloF
o7JvgMWGp7gBk1Mvrs8eNuwRlmZALiCl1EDBAtpwtPO4ntIMZ0o8TG1cspsCYX/utviUtK9PNnh2
9JLZt36MI1gEG/bALJnZt5j7zi7+zz+ZcnNNPQBczgAAAABJRU5ErkJggg==
)
C.4
D.4
-
如图所示在△ABC中,sin2A+sin2C=sin2B+sinA.sinC
(1)求B的度数.
(2)设H为△ABC的垂心,且
•
=6求AC边长的最小值.
-
在△ABC中,给出下列四个命题:①若sin2A=sin2B,则△ABC为等腰三角形;
②若sinA=cosB,则△ABC是直角三角形;
③若cosA•cosB•cosC<0,则△ABC是钝角三角形;
④若cos(A-B)•cos(B-C)•cos(C-A)=1,则△ABC是等边三角形.
以上命题正确的是________(填命题序号).
-
在△ABC中,给出下列四个命题:①若sin2A=sin2B,则△ABC为等腰三角形;
②若sinA=cosB,则△ABC是直角三角形;
③若cosA•cosB•cosC<0,则△ABC是钝角三角形;
④若cos(A-B)•cos(B-C)•cos(C-A)=1,则△ABC是等边三角形.
以上命题正确的是________(填命题序号).
-
在△ABC中,给出下列四个命题:
①若sin2A=sin2B,则△ABC必是等腰三角形;
②若sinA=cosB,则△ABC必是直角三角形;
③若cosA•cosB•cosC<0,则△ABC必是钝角三角形;
④若cos(A-B)•cos(B-C)•cos(C-A)=1,则△ABC必是等边三角形.
以上命题中正确的命题的个数是( )
A.1
B.2
C.3
D.4