已知sinα=$\frac{1}{3}$+cosα，且α∈（0，$\frac{\mathrm{\pi }}{2}$），则$\frac{\cos 2\alpha }{\sin \left(\alpha +\frac{\mathrm{\pi }}{4}\right)}$的值为____ 

    Have you ever thought about your life after you grow up? It is not easy --- that's what some US students say after they try out adult (成年人) life at school.

    Mount Logan Middle School, Utah, has an activity called Reality Town. Each student gets a “job” and some money. The higher the grade (成绩), the better the job they can get. Then, they have to pay for different things in the real world, such as transportation (交通) and groceries . Some of them have a “husband (丈夫)” or a “wife” and maybe a few “kids”. Student Jason Peisley, 13, became a father with a 5-year-old girl. The hardest part for him was paying taxes (税).“I make $90,000 (571,000 yuan), but after I pay my taxes, I only have $66,000 left,” he said. “Life isn't easy. There are a lot of things to pay for.” “It's a wake up call for these students,” said Greg Aullman, a teacher at Mount Logan, “to learn how much it costs to live. So, they'll study harder than before and love their parents more. ”