Use the fundamental identities to simplify the expression.
9tantheta9cottheta/9sectheta

[9tan(θ) * 9cot(θ)] / 9sec(θ)

First cancel out the 9's:

tan(θ)cot(θ)/sec(θ)

Recall the following trig identities:

tan = sin/cos

cot = cos/sin

sec = 1/cos

Thus, we can rewrite the expression as:

[ (Sin(θ)/cos(θ)) *(cos(θ)/sin(θ)) ] / (1/cos(θ))

In the numerator, the sine's and cosine's cancel each other out:

1 / (1/cos(θ))

which we can rewrite as cos(θ).