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).