Algebra Examples

$\tan (θ) \cot (θ) = 1$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Reorder $\tan (θ)$ and $\cot (θ)$ .

$\cot (θ) \tan (θ) = 1$

Step 1.1.2

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

$\frac{\cos (θ)}{\sin (θ)} \cdot \frac{\sin (θ)}{\cos (θ)} = 1$

Step 1.1.3

Cancel the common factors.

$1 = 1$

Step 2

Since $1 = 1$ , the equation will always be true.

Always true

Step 3

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$