指同一个人a singer and dancer较为常见，但也可以用a singer and a dancer。一般说来，并列的两个名词指同一人，后一名词之前通常不用冠词，但有时为了强调，可用冠词。例如：

She's an English teacher and a mother of two children. 她是英语教师，还是两个孩子的母亲。《柯林斯高阶英汉双解词典》

▲关于并列名词前的冠词使用问题，还需注意以下几点：

1）用or连接两个不同身份或职业的名词时，第二个名词前常省略冠词。例如：

A medical examination without a doctor or nurse in the room? （1984版《高中英语第一册》LESSON 2  AT HOME IN THE FUTURE）

The children must cross the road only with a teacher or parent. 孩子们必须和老师或父（母）亲一起过马路。《简明英汉词典》

2） and连接两个性别不同的人时，第二个名词前可省略冠词。例如：

The king and queen had fled. 国王和王后都逃之夭夭了。《柯林斯高阶英汉双解词典》

At a table inside, a man and woman were awaiting her. 在里面的一张桌子旁，一男一女正等着她。《柯林斯高阶英汉双解词典》

3）在指两个人时，若一个名词与另一个具有相反意义的名词并列，可用或不用冠词。例如：

She spent the post-war years of her marriage trying to reunite father and son. 在战后几年的婚姻生活中，她千方百计想让父子团聚。《柯林斯高阶英汉双解词典》

The birth took place this morning, and both (the) mother and (the) child are doing well.（夸克《英语语法大全》）

Is 'a singer and dancer' the same as 'a singer and a dancer'？（The former refers to the same person, while the latter indicates two people.）

Is 'the book and chair' the same as 'the book and the chair'？（The former is false, while the latter is correct.）

Is 'in summer and winter' the same as' in summer and in winter'？（Both are true, but the former is preferred. This problem involves omitting the preposition rather than the article.）

Is 'the begging of the story and the novel' the same as 'the begging of the story and of the novel'？（I'm confused about your question. What's the meaning of begging?）

我的理解和刘老师解答有所不同。

a singer and dancer可以=a singer and a dancer. 可以指同一个人。

一句名人名言： I was always a singer and a dancer, and I always wanted to be an actress. For me, it's all just one thing.

https://www.brainyquote.com/quotes/jennifer_lopez_129516

The book and chair 在特定语境也不存在。如果书在椅子上，老师让人连书和椅子一同搬过来，就可以这样用。 没见过

in summer and winter， 如果重复in, 是表示强调。the beginning of the story and of the novel. 同理。