Trigonometry Examples

$\csc^{4} (x) - \cot^{4} (x)$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $\csc^{4} (x)$ as ${(\csc^{2} (x))}^{2}$ .

${(\csc^{2} (x))}^{2} - \cot^{4} (x)$

Step 1.2

Rewrite $\cot^{4} (x)$ as ${(\cot^{2} (x))}^{2}$ .

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \csc^{2} (x)$ and $b = \cot^{2} (x)$ .

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

Step 3

Apply pythagorean identity.

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

Step 4

Multiply $\csc^{2} (x) + \cot^{2} (x)$ by $1$ .

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

Step 5

The polynomial cannot be factored using the specified method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the specified method.