Algebra Examples

$\frac{\tan (θ)}{\sin (θ)} = \sec (θ)$

Step 1

Start on the left side.

$\frac{\tan (θ)}{\sin (θ)}$

Step 2

Write $\tan (θ)$ in sines and cosines using the quotient identity.

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

$\frac{1}{\cos (θ)}$

Step 4

Rewrite $\frac{1}{\cos (θ)}$ as $\sec (θ)$ .

$\sec (θ)$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$\frac{\tan (θ)}{\sin (θ)} = \sec (θ)$ is an identity