Algebra Examples

$\frac{1 - \csc (- θ)}{\csc (- θ)}$

Step 1

Simplify the numerator.

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Step 1.1

Since $\csc (- θ)$ is an odd function, rewrite $\csc (- θ)$ as $- \csc (θ)$ .

$\frac{1 - - \csc (θ)}{\csc (- θ)}$

Step 1.2

Multiply $- - \csc (θ)$ .

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

$\frac{1 + 1 \csc (θ)}{\csc (- θ)}$

Step 1.2.2

Multiply $\csc (θ)$ by $1$ .

$\frac{1 + \csc (θ)}{\csc (- θ)}$

Step 2

Since $\csc (- θ)$ is an odd function, rewrite $\csc (- θ)$ as $- \csc (θ)$ .

$\frac{1 + \csc (θ)}{- \csc (θ)}$

Step 3

Move the negative in front of the fraction.

$- \frac{1 + \csc (θ)}{\csc (θ)}$