共50条信息
在\(\triangle ABC\)中,\(BC\)边上的中线长等于\(BC\)长的\(2\)倍,则\(\dfrac{\sin B·\sin C}{\sin 2A} \)的最大值为_____________
已知:\({\sin }^{2}{30}^{^{\circ}}+{\sin }^{2}90^{\circ}+{\sin }^{2}150^{\circ}= \dfrac{3}{2}{\sin }^{2}5^{\circ}+{\sin }^{2}60^{\circ}+{\sin }^{2}125^{\circ}= \dfrac{3}{2} .\)通过观察上述两等式的规律,写出一般性的命题:_____________________\( = \dfrac{3}{2} \).
\( \dfrac{1}{2\sin 10^{\circ}}-2\sin 70^{\circ}= \) .
已知等差数列\(\{a_{n}\}\)的公差\(d∈(0,1)\),且\(\dfrac{{{\sin }^{2}}{{a}_{3}}-{{\sin }^{2}}{{a}_{7}}}{\sin ({{a}_{3}}+{{a}_{7}})}=-1\),当\(n=10\)时,数列\(\{a_{n}\}\)的前\(n\)项和\(S_{n}\)取得最小值,则首项\(a_{1}\)的取值范围是
求值:
\((1)\sin 50{}^\circ (1+\sqrt{3}\sin 10{}^\circ )\)
\((2)\dfrac{2{{\cos }^{2}}42{}^\circ +\sin 75{}^\circ \cos 81{}^\circ -1}{\cos 6{}^\circ -\cos 75{}^\circ \cos 81{}^\circ }\)
进入组卷