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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,在矩形
ABCD中,
AB=2
AD=2,
O為
CD的中點(diǎn),沿
AO將△
AOD折起,使
DB=
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.
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(1)求證:平面
AOD⊥平面
ABCO;
(2)求直線
BC與平面
ABD所成角的正弦值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,在多面體ABCDE中,DB⊥平面ABC,AE∥DB,且△ABC是邊長為2的等邊三角形,AE=1,CD與平面ABDE所成角的正弦值為
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.
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(Ⅰ)若F是線段CD的中點(diǎn),證明:EF⊥面DBC;
(Ⅱ)求二面角D-EC-B的平面角的余弦值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分12分) 四棱錐S-ABCD中,底面ABCD為平行四邊形,側(cè)面SBC⊥底面ABCD.已知∠ABC=45°,AB=2,BC=
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,SA=SB=
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。

(1)證明:SA⊥BC;
(2)求直線SD與平面SAB所成角的大��;
(3)求二面角D-SA-B的大�。�
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,矩形
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中,
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,
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,

平面
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,
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,
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,
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為

的中點(diǎn).

(1)求證:

平面

.
(2)若
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,求平面

與平面

所成銳二面角的余弦值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,四邊形ABCD中,
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為正三角形,
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,

,AC與BD交于O點(diǎn).將

沿邊AC折起,使D點(diǎn)至P點(diǎn),已知PO與平面ABCD所成的角為

,且P點(diǎn)在平面ABCD內(nèi)的射影落在
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內(nèi).
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(Ⅰ)求證:
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平面PBD;
(Ⅱ)若
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時,求二面角

的余弦值。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,在正方體
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中,
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是棱
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的中點(diǎn),

在棱
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上.
且
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,若二面角

的余弦值為
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,求實(shí)數(shù)

的值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知直三棱柱
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中,△
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為等腰直角三角形,∠
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=90°,且
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=
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,
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、
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、
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分別為
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、
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、

的中點(diǎn).

(1)求證:

∥平面

;
(2)求證:

⊥平面

;
(3)求二面角

的余弦值
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知空間四面體

的每條邊都等于1,點(diǎn)
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分別是

的中點(diǎn),則
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等于 �。� )
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