已知 $\alpha \in R,\sin \alpha +2cos\alpha =\frac{\sqrt{10}}{2}$ ，则tan2α=（   ）

Dear Liz,

    Thank you very much ____ your letter and the photos of your ____(friend) and family. Your parents and friends look really nice ____ the photo. Now I can tell you something about me and ____ family here in New York.

    I've got two brothers. ____(they) names are Lukas and Andreas and they ____(be) 16 and 19. My mother is French and her name is Christine. Dad is American and his name's Dieter. Our house ____(have) got four bedrooms and a small garden. My room is tidy, but my ____(brother) is not. They don't often clean it. We have a dog, Zak, and we think he's cute. We ____(love) it a lot.

    Please tell me all about ____ friends and school in your next letter. I'd like to know about English schools.

Love,

Laura

闻名全球的“杂交水稻之父”袁隆平，在不断创新杂交水稻技术之余，看书和听音乐是他的两大爱好，除此之外排球、游泳、飙车也样样在行。这些对于他的科研工作有很大的帮助和促进。这表明（    ）