共50条信息
若\(z=\sin \theta -\dfrac{3}{5}+(\cos \theta -\dfrac{4}{5})i\)是纯虚数，则\(\tan (\theta -\dfrac{\pi }{4})\)的值为\((\) \()\)
\(\cos {263}^{0}\cos {203}^{0}+\sin {83}^{0}\sin {23}^{0} \)的值为\((\) \()\)
\(\dfrac{\tan 75{}^\circ -1}{1+\tan 75{}^\circ }=(\) \()\)
在\(\triangle ABC\)中，内角\(A\)，\(B\)，\(C\)所对的边分别为\(a\)，\(b\)，\(c\)，且\(\dfrac{a}{b}=1+\cos C\)．
\((1)\)求证：\(\sin C=\tan B\)；
\((2)\)若\(\cos B=\dfrac{2\sqrt{7}}{7}\)，\(C\)为锐角，\(\triangle ABC\)的面积为\(\dfrac{3\sqrt{3}}{2}\)，求\(c\)．
\(\sin 18^{{∘}}\cos 12^{{∘}}{+}\cos 18^{{∘}}\sin 12^{{∘}}{=}(\) \()\)
设函数\(f\left(x\right)=\cos \left(x+ \dfrac{2}{3}π\right)+2{\cos }^{2} \dfrac{x}{2},x∈R \)．
\((1)\)求\(f(x)\)的值域；
\((2)\)记\(\Delta ABC\)的内角\(A\)，\(B\)，\(C\)的对边长分别为\(a\)，\(b\)，\(c\)，若\(f(B)=1\)，\(b=1,c= \sqrt{3} \)，求\(a\)的值．
若\(\cos \alpha =-\dfrac{4}{5}\)，\(\alpha \)是第三象限的角，则\(\sin (\alpha +\dfrac{\pi }{4}) =(\) \()\)
已知\(θ\)\(∈\left(\begin{matrix} \begin{matrix}0, \dfrac{π}{4} \end{matrix}\end{matrix}\right)\)，且\(\sin \)\(θ\)\(-\cos \)\(θ\)\(=-\dfrac{\sqrt{14}}{4}\)，则\( \dfrac{2\cos ^{2}θ-1}{\cos \left(\begin{matrix} \begin{matrix} \dfrac{π}{4}+θ \end{matrix}\end{matrix}\right)}\)等于 \((\) \()\)
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