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            • 1. 已知函数\(f(x)=2{\sin }^{2}⁡(x+ \dfrac{π}{4})− \sqrt{3}\cos ⁡2x,x∈[ \dfrac{π}{4}, \dfrac{π}{2}]. \)
              \((\)Ⅰ\()\)求\(f(x)\)的值域;
              \((\)Ⅱ\()\)若不等式\({|}f(x){-}m{|} < 2\)在\(x{∈[}\dfrac{\pi}{4}{,}\dfrac{\pi}{2}{]}\)上恒成立,求实数\(m\)的取值范围.
            • 2.

              若\(\dfrac{\sqrt{2}\cos 2\theta }{\cos (\dfrac{\pi }{4}+\theta )}=\sqrt{3}\sin 2\theta \),则\(\sin 2\theta =\)

              A.\(\dfrac{1}{3}\)
              B.\(\dfrac{2}{3}\)
              C.\(-\dfrac{2}{3}\)
              D.\(-\dfrac{1}{3}\) 
            • 3.

              在\(\Delta ABC\)中,角\(A,B,C\)的对边分别为\(a,b,c,\cos C=\dfrac{3}{10}\).

              \((1)\)若\(\overrightarrow{CA}\bullet \overrightarrow{CB}=\dfrac{9}{2}\),求\(\Delta ABC\)的面积;

              \((2)\)设向量\( \overset{⇀}{x}=(2\sin ⁡B,− \sqrt{3}), \overset{⇀}{y}=(\cos ⁡2B,1−2{\sin }^{2} \dfrac{B}{2}) \),且\( \overset{⇀}{x}/\!/ \overset{⇀}{y} \),求角\(B\)的值.

            • 4.
              已知\(\sin α-\cos α= \dfrac {1}{5}\),则\(\sin 2α=\) ______ .
            • 5.
              在\(\triangle ABC\)中,\(\cos ( \dfrac {π}{4}+A)= \dfrac {5}{13}\),则\(\sin 2A=\) ______ .
            • 6.
              已知\(\sin α=2\sin β\),\(\tan α=3\tan β\),则\(\cos 2α=\) ______ .
            • 7.
              已知\( \dfrac {2\sin α+\cos α}{\sin \alpha -\cos \alpha }=3\),则\(\tan 2α=\) ______ .
            • 8.

              \((1)\int _{0}^{1}( \sqrt{1-{x}^{2}}+x+{x}^{3})dx \) ______      

              \((2)\)求值:\( \dfrac{\cos 20^{\circ}}{\cos 35^{\circ} \sqrt{1-\sin 20^{\circ}}} \) \(=\) ______         

              \((3)\)已知\(m\),\(n\),\(p\)表示不重合的三条直线,\(α\),\(β\),\(γ\)表示不重合的三个平面\(.\)下列说法正确的是 ______       \(.(\)写出所有正确命题的序号\()\).
              \(①\)若\(m⊥p\),\(m/\!/n\),则\(n⊥p\);
              \(②\)若\(m/\!/β\),\(n/\!/β\),\(m⊂α\),\(n⊂α\),则\(α/\!/β\);
              \(③\)若\(α⊥γ\),\(β⊥γ\),\(α∩β=m\),则\(m⊥γ\);
              \(④\)若\(α/\!/β\),\(m⊂α\),\(n⊂β\),则\(m/\!/n\).

              \((4)\)设函数\(y=f(x)\)的定义域为\(D\),若对于任意\(x_{1}\),\(x_{2}∈D\),当\(x_{1}+x_{2}=2a\)时,恒有\(f(x_{1})+f(x_{2})=2b\),则称点\((a,b)\)为函数\(y=f(x)\)图象的对称中心,研究函数\(f(x)=x^{3}+\sin x+2\)的图象的某一个对称点,并利用对称中心的上述定义,可得到\(f(-1)+f(- \dfrac{9}{10})+⋯+f(0)+⋯+f( \dfrac{9}{10})+f(1)= \)___           

            • 9.

              已知,则\(\cos (2α+ \dfrac{3π}{5}) \)

              A.\(- \dfrac{7}{9} \)
              B.\(- \dfrac{1}{9} \)
              C.\( \dfrac{1}{9} \)
              D.\( \dfrac{7}{9} \)
            • 10.

              已知向量\(\overrightarrow{m}=(\sqrt{3}\sin 2x-1,\cos x),\overrightarrow{n}=(1,2\cos x)\),设函数\(f(x)=\overrightarrow{m}\cdot \overrightarrow{n}\)

              \((1)\)求\(f(x) \)的最小正周期与单调递减区间

              \((2)\)在\(\triangle ABC \)中,\(a,b,c \)分别是角\(A,B,C \)的对边,若\(f(A)=1,b=1,\Delta ABC\)的面积为\( \dfrac{ \sqrt{3}}{2} \),求\(a \)的值。

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