Linear Algebra Examples

$2 \cot^{2} (3 x) = 7 \csc (3 x - 5)$

Step 1

Set the argument in $\cot (3 x)$ equal to $π n$ to find where the expression is undefined.

$3 x = π n$ , for any integer $n$

Step 2

Divide each term in $3 x = π n$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x = π n$ by $3$ .

$\frac{3 x}{3} = \frac{π n}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{π n}{3}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{π n}{3}$

Step 3

The domain is all values of $x$ that make the expression defined.

Set-Builder Notation:

${x | x \neq \frac{π n}{3}}$ , for any integer $n$

Step 4