共50条信息
已知函数\(f(x)= \sqrt{3}\cos (2x- \dfrac{π}{3})-2\sin x\cos x \)．
\((I)\)\(f\)\((\)\(x\)\()\)的最小正周期；
\((II)\)求证：当\(x∈[- \dfrac{π}{4}, \dfrac{π}{4}] \)时，\(f(x)\geqslant - \dfrac{1}{2} \)．
已知\(\alpha \in (0,\pi ),\sin \alpha +\cos \alpha =\dfrac{1}{5}\)．
\((\)Ⅰ\()\) 求\(\sin \alpha -\cos \alpha \)的值；
\((\)Ⅱ\()\) 求\(\sin (2\alpha +\dfrac{\pi }{3})\)的值．
用单位圆证明角\(α\)的正弦的绝对值与余弦的绝对值之和不小于\(1\)，即已知\(0\leqslant α < 2π\)，求证：\(|\sin α|+|\cos α|\geqslant 1\)．
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