This is for my trig class, and the directions say to verify the identity. Thanks so much.

Use the identities tan(x) = sin(x)/cos(x) and csc(x) = 1/sin(x) to get:

1/(tan(x) × csc(x)) = 1/[(sin(x)/cos(x) × 1/sin(x)]

Now just work with the denominator (bottom) of the rational expression (fraction):

sin(x)/cos(x) × 1/sin(x) = 1/cos(x)

Now we have

1/(1/cos(x) = 1 ÷ 1/cos(x) = 1× cos(x) = cos(x):