Simplify cot(x)^2csc(x)^2-cot(x)^2

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Rearrange terms.

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

Step 6

Apply pythagorean identity.

$\cot^{2} (x) \cdot \cot^{2} (x)$

Step 7

Multiply $\cot^{2} (x)$ by $\cot^{2} (x)$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

$\cot^{4} (x)$