Precalculus Examples

$\log_{3} (\tan (x)) + \log_{3} (\cot (x))$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (\tan (x) \cot (x))$

Step 2

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

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Step 2.1

Reorder $\tan (x)$ and $\cot (x)$ .

$\log_{3} (\cot (x) \tan (x))$

Step 2.2

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

$\log_{3} (\frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)})$

Step 2.3

Cancel the common factors.

$\log_{3} (1)$

Step 3

Logarithm base $3$ of $1$ is $0$ .

$0$