[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).
