I'm never sure how far to go on these questions but I think what I'e done looks pretty nice. Essentially I simplified each radical, factored out each variable, combined the radicals after more simplification, and then picked the answer you were most likely looking for. I gave some alternatives in my work that are "simple" too, but the answer above is most likely I'd say.
Work is in the attachment, comment with any questions.
1 ) cot x * sin x = cos x (cos x / sin x) * sin x = cos x cos x = cos x Answer: B ) cot x = cos x / sin x 2 ) ( sin² x + cos² x ) / cos x = sec x 1/cos x = sec x sec x = sec x Answer: C ) cos² x + sin² x = 1