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如图,平面四边形
ABCD中,

,

,

,

,

,点
E,
F满足

,

,将

沿
EF对折至

,使得

.

(1)证明:

;
(2)求面
PCD与面
PBF所成的二面角的正弦值.
已知函数

.
(1)当

时,求曲线

在点

处的切线方程;
(2)若

有极小值,且极小值小于0,求
a的取值范围.
记

的内角
A,
B,
C的对边分别为
a,
b,
c,已知

.
(1)求
A.
(2)若

,

,求

的周长.
抛物线
C:

的准线为
l,
P为
C上的动点,过
P作

的一条切线,
Q为切点,过
P作
l的垂线,垂足为
B,则(
)
A.l与 相切 |
B.当P,A,B三点共线时, |
C.当 时, |
D.满足 的点 有且仅有2个 |
已知正三棱台

的体积为

,

,

,则

与平面
ABC所成角的正切值为(
)
A. | B.1 | C.2 | D.3 |
设函数

,

,当

时,曲线

与

恰有一个交点,则

(
)
A. | B. | C.1 | D.2 |
如图,四棱锥

中,

底面
ABCD,

,

.

(1)若

,证明:

平面

;
(2)若

,且二面角

的正弦值为

,求

.
已知

和

为椭圆

上两点.
(1)求
C的离心率;
(2)若过
P的直线

交
C于另一点
B,且

的面积为9,求

的方程.