Simplify (cot(A)-1)(cot(A)+1)

$(\cot (A) - 1) (\cot (A) + 1)$

Step 1

Expand $(\cot (A) - 1) (\cot (A) + 1)$ using the FOIL Method.

Apply the distributive property.

$\cot (A) (\cot (A) + 1) - 1 (\cot (A) + 1)$

Apply the distributive property.

$\cot (A) \cot (A) + \cot (A) \cdot 1 - 1 (\cot (A) + 1)$

Apply the distributive property.

$\cot (A) \cot (A) + \cot (A) \cdot 1 - 1 \cot (A) - 1 \cdot 1$

Step 2

Simplify terms.

Combine the opposite terms in $\cot (A) \cot (A) + \cot (A) \cdot 1 - 1 \cot (A) - 1 \cdot 1$ .

Reorder the factors in the terms $\cot (A) \cdot 1$ and $- 1 \cot (A)$ .

$\cot (A) \cot (A) + 1 \cot (A) - 1 \cot (A) - 1 \cdot 1$

Subtract $1 \cot (A)$ from $1 \cot (A)$ .

$\cot (A) \cot (A) + 0 - 1 \cdot 1$

Add $\cot (A) \cot (A)$ and $0$ .

$\cot (A) \cot (A) - 1 \cdot 1$

Simplify each term.

Multiply $\cot (A) \cot (A)$ .

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

$\cot^{1} (A) \cot (A) - 1 \cdot 1$

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

$\cot^{1} (A) \cot^{1} (A) - 1 \cdot 1$

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

${\cot (A)}^{1 + 1} - 1 \cdot 1$

Add $1$ and $1$ .

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

Multiply $- 1$ by $1$ .

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