Solve for θ tan(theta)cot(theta)=1

$\tan (θ) \cot (θ) = 1$

Simplify the left side.

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

Reorder $\tan (θ)$ and $\cot (θ)$ .

$\cot (θ) \tan (θ) = 1$

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

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

Cancel the common factors.

$1 = 1$

Since $1 = 1$ , the equation will always be true for any value of $θ$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$