天壹名校联盟2023下学期高二期末考试·数学.考卷答案试卷答案,我们目前收集并整理关于天壹名校联盟2023下学期高二期末考试·数学.考卷答案得系列试题及其答案，更多试题答案请关注微信公众号：考不凡/直接访问www.kaobufan.com(考不凡)
天壹名校联盟2023下学期高二期末考试·数学.考卷答案试卷答案
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分析直接将原式的分子分母同时乘以：sin$\frac{x}{2}$+cos$\frac{x}{2}$，再运用倍角公式和降幂公式对该式进行化简．
解答解：因为x∈（0，π），所以cos$\frac{x}{2}$＞0，
原式=$\frac{（1+sinx+cosx）（sin\frac{x}{2}-cos\frac{x}{2}）（sin\frac{x}{2}+cos\frac{x}{2}）}{cos\frac{x}{2}（sin\frac{x}{2}+cos\frac{x}{2}）}$
=-$\frac{（1+sinx+cosx）•cosx}{cos\frac{x}{2}sin\frac{x}{2}+cos^2\frac{x}{2}}$
=-$\frac{（1+sinx+cosx）cosx}{\frac{1}{2}sinx+\frac{1}{2}（1+cosx）}$
=-$\frac{2（1+sinx+cosx）cosx}{1+sinx+cosx}$
=-2cosx，
即原式=-2cosx．
点评本题主要考查了三角函数恒等变换的应用，涉及到正弦和余弦的倍角公式，降幂公式的运用，属于中档题．
