Precalculus Examples

$\csc^{3} (x) - \csc (x) \cot^{2} (x)$

Step 1

Factor $\csc (x)$ out of $\csc^{3} (x) - \csc (x) \cot^{2} (x)$ .

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Step 1.1

Factor $\csc (x)$ out of $\csc^{3} (x)$ .

$\csc (x) \csc^{2} (x) - \csc (x) \cot^{2} (x)$

Step 1.2

Factor $\csc (x)$ out of $- \csc (x) \cot^{2} (x)$ .

$\csc (x) \csc^{2} (x) + \csc (x) (- 1 \cot^{2} (x))$

Step 1.3

Factor $\csc (x)$ out of $\csc (x) \csc^{2} (x) + \csc (x) (- 1 \cot^{2} (x))$ .

$\csc (x) (\csc^{2} (x) - 1 \cot^{2} (x))$

Step 2

Apply pythagorean identity.

$\csc (x) \cdot 1$

Step 3

Multiply $\csc (x)$ by $1$ .

$\csc (x)$