Trigonometry Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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Step 1.1.1

Multiply by $1$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Reorder $1$ and $- \csc^{2} (x)$ .

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

Step 1.3

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

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

Step 1.4

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 1.5

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

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Step 4.1

Move $\cot^{2} (x)$ .

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

Step 4.2

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

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Step 4.2.1

Raise $\cot (x)$ to the power of $1$ .

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

Step 4.2.2

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

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

Step 4.3

Add $2$ and $1$ .

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