Trigonometry Examples

$\frac{\cot (x)}{\tan (x)} = \tan^{2} (x)$

Step 1

Simplify $\frac{\cot (x)}{\tan (x)}$ .

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Step 1.1

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

$\frac{\cot (x)}{\frac{\sin (x)}{\cos (x)}} = \tan^{2} (x)$

Step 1.2

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

$\frac{\frac{\cos (x)}{\sin (x)}}{\frac{\sin (x)}{\cos (x)}} = \tan^{2} (x)$

Step 1.3

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

$\frac{\cos (x)}{\sin (x)} \cdot \frac{\cos (x)}{\sin (x)} = \tan^{2} (x)$

Step 1.4

Simplify.

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Step 1.4.1

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

$\cot (x) \frac{\cos (x)}{\sin (x)} = \tan^{2} (x)$

Step 1.4.2

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

$\cot (x) \cot (x) = \tan^{2} (x)$

Step 1.4.3

Raise $\cot (x)$ to the power of $1$ .

$\cot^{1} (x) \cot (x) = \tan^{2} (x)$

Step 1.4.4

Raise $\cot (x)$ to the power of $1$ .

$\cot^{1} (x) \cot^{1} (x) = \tan^{2} (x)$

Step 1.4.5

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

${\cot (x)}^{1 + 1} = \tan^{2} (x)$

Step 1.4.6

Add $1$ and $1$ .

$\cot^{2} (x) = \tan^{2} (x)$

Step 2

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

$x = \frac{π}{4} + \frac{π n}{2}$ , for any integer $n$

Step 3