Precalculus Examples

$\cot (x) \sin (x) + \cot (x) = 0$

Step 1

Simplify $\cot (x) \sin (x) + \cot (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1.1

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

$\frac{\cos (x)}{\sin (x)} \sin (x) + \cot (x) = 0$

Step 1.1.1.2

Cancel the common factors.

$\cos (x) + \cot (x) = 0$

Step 1.1.2

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

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

Step 1.2

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

$\cos (x) + \cot (x) = 0$

Step 2

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

$x \approx \frac{π}{2} + 4 π n, 4.7125 + 4 π n, \frac{5 π}{2} + 4 π n, 10.9953125 + 4 π n$ , for any integer $n$

Step 3