Evaluate (tan(theta))/(sec(theta))

$\frac{\tan (θ)}{\sec (θ)}$

Step 1

Rewrite $\sec (θ)$ in terms of sines and cosines.

$\frac{\tan (θ)}{\frac{1}{\cos (θ)}}$

Step 2

Rewrite $\tan (θ)$ in terms of sines and cosines.

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\frac{1}{\cos (θ)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (θ)}$ .

$\frac{\sin (θ)}{\cos (θ)} \cos (θ)$

Step 4

Write $\cos (θ)$ as a fraction with denominator $1$ .

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{\cos (θ)}{1}$

Step 5

Cancel the common factor of $\cos (θ)$ .

Cancel the common factor.

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{\cos (θ)}{1}$

Rewrite the expression.

$\sin (θ)$