Trigonometry Examples

$\frac{\tan (θ)}{\cot (θ)}$

Step 1

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

$\frac{\tan (θ)}{\frac{\cos (θ)}{\sin (θ)}}$

Step 2

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

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\frac{\cos (θ)}{\sin (θ)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (θ)}{\sin (θ)}$ .

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

Step 4

Simplify.

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Step 4.1

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\tan (θ) \frac{\sin (θ)}{\cos (θ)}$

Step 4.2

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\tan (θ) \tan (θ)$

Step 4.3

Raise $\tan (θ)$ to the power of $1$ .

$\tan^{1} (θ) \tan (θ)$

Step 4.4

Raise $\tan (θ)$ to the power of $1$ .

$\tan^{1} (θ) \tan^{1} (θ)$

Step 4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\tan (θ)}^{1 + 1}$

Step 4.6

Add $1$ and $1$ .

$\tan^{2} (θ)$