已知向量$\overrightarrow{m}$=（cos$\frac{x}{2}$，﹣1），$\overrightarrow{n}$=（$\sqrt{3}$sin$\frac{x}{2}$，cos²$\frac{x}{2}$），设函数f（x）=$\overrightarrow{m}$$·$$\overrightarrow{n}$+1．

（1）求函数f（x）的单调递增区间；

（2）在△ABC中，角A，B，C的对边分别为a，b，c，且满足a²+b²=6abcosC，sin²C=2sinAsinB，求f（C）的值．

                                     C

    People call the Winter Olympics the White Olympics. At this time, they publish(发行) many stamps to mark(标志) the great games. The first stamps came out on January 25th, 1932 in the United States for the 3rd White Olympics. From then on, publishing stamps during the White Olympics became a rule.

    During the 4th Winter Olympics, people published a group of stamps in November 1936. They drew five rings of Olympics. It was the first time that the rings appeared(出现) on the stamps of the White Olympics.

    In the 1950s，the stamps of this kind became more colorful. When the White Olympics came, the host countries as well as non-host countries published stamps to mark those games. China also published four stamps in February 1980 when the Chinese sportsmen began to take part in the White Olympics.

    In Asia, Japan was the only country to hold the White Olympics. They sold 14,500 million stamps during the Olympics.

    People drew different kinds of sports on these small stamps, and they enjoyed the wonderful sports and some famous players.

      默写。
     ①晓战随金鼓，                     。（唐·李白《塞下曲》）
     ②                     ，春风不度玉门关。（唐·王之涣《凉州词》）
     ③蒌蒿满地芦芽短，                     。（宋·苏轼《惠崇<春江晚景>二首》）
     ④                     ，君子好逑。（《关雎》）
     ⑤剪不断，理还乱，是离愁。                       。（南唐·李煜《相见欢》）
     ⑥山回路转不见君，                     。（唐·岑参《白雪歌送武判官归京》）
     ⑦登斯楼也，则有去国怀乡，              ，              ，感极而悲者矣。 （宋·范仲淹《岳阳楼记》）