9 csc x / csc x − cot x = 9 csc x(csc x + cot x)

Question

Verify the identity.

Use a Pythagorean Identity, and then simplify.

Answer 1

9 csc x/(csc x - cot x) =

9 csc x/(csc x - cot x) * (csc x + cot x)/(csc x + cot x) =

9 csc x (csc x + cot x)/(csc²x - cot²x) =

9 csc x (csc x + cot x)/1 =

9 csc x (csc x + cot x)