<p>actually, there’s nothing wrong at all with “performing for.” it’s not even awkward. the sentence uses an elliptical construction to omit the verb “are” after the word “dancers,” which turns the second half of the sentence into a dependent clause, which makes it okay to use a comma to separate the two clauses.</p>
<p>in other words, if the sentence were written this way, it would be fine:</p>
<p>“Ballet, modern dance, and Indian classical dance are forms of theater dance; the dancers are usually highly trained professionals performing for audiences in particular venues and on special occasions.”</p>
<p>which means you can take out the second “are” and create this sentence:</p>
<p>“Ballet, modern dance, and Indian classical dance are forms of theater dance, the dancers usually highly trained professionals performing for audiences in particular venues and on special occasions.”</p>
<p>i doubt you’ll be called upon to make this transformation on the SAT. indeed, on this question you don’t even have to realize that it’s okay, since (a) is clearly wrong and you can only have one wrong thing per question.</p>