Trigonometry Examples

$(\cot (x) + 1) (\csc (x) - \frac{1}{2}) = 0$

Step 1

Simplify $(\cot (x) + 1) (\csc (x) - \frac{1}{2})$ .

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Step 1.1

Expand $(\cot (x) + 1) (\csc (x) - \frac{1}{2})$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$\cot (x) (\csc (x) - \frac{1}{2}) + 1 (\csc (x) - \frac{1}{2}) = 0$

Step 1.1.2

Apply the distributive property.

$\cot (x) \csc (x) + \cot (x) (- \frac{1}{2}) + 1 (\csc (x) - \frac{1}{2}) = 0$

Step 1.1.3

Apply the distributive property.

$\cot (x) \csc (x) + \cot (x) (- \frac{1}{2}) + 1 \csc (x) + 1 (- \frac{1}{2}) = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $\cot (x)$ and $\frac{1}{2}$ .

$\cot (x) \csc (x) - \frac{\cot (x)}{2} + 1 \csc (x) + 1 (- \frac{1}{2}) = 0$

Step 1.2.2

Multiply $\csc (x)$ by $1$ .

$\cot (x) \csc (x) - \frac{\cot (x)}{2} + \csc (x) + 1 (- \frac{1}{2}) = 0$

Step 1.2.3

Multiply $- \frac{1}{2}$ by $1$ .

$\cot (x) \csc (x) - \frac{\cot (x)}{2} + \csc (x) - \frac{1}{2} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{3 π}{4} + π n$ , for any integer $n$

Step 3