Algebra Examples

$\cos (x) \cdot \csc (x) - 2 \cos (x) = 0$

Step 1

Simplify $\cos (x) \cdot \csc (x) - 2 \cos (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $\csc (x)$ in terms of sines and cosines.

$\cos (x) \cdot \frac{1}{\sin (x)} - 2 \cos (x) = 0$

Step 1.1.2

Combine $\cos (x)$ and $\frac{1}{\sin (x)}$ .

$\frac{\cos (x)}{\sin (x)} - 2 \cos (x) = 0$

Step 1.2

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\cot (x) - 2 \cos (x) = 0$

Step 2

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

$x = \frac{π}{6} + 2 π n, \frac{π}{2} + 2 π n, \frac{5 π}{6} + 2 π n, \frac{3 π}{2} + 2 π n$ , for any integer $n$

Step 3