Trigonometry Examples

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

Step 1

Subtract $\tan^{2} (x)$ from both sides of the equation.

$\frac{\tan (x)}{\cot (x)} - \tan^{2} (x) = 0$

Step 2

Simplify $\frac{\tan (x)}{\cot (x)} - \tan^{2} (x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{\tan (x)}{\frac{\cos (x)}{\sin (x)}} - \tan^{2} (x) = 0$

Step 2.1.2

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

$\frac{\frac{\sin (x)}{\cos (x)}}{\frac{\cos (x)}{\sin (x)}} - \tan^{2} (x) = 0$

Step 2.1.3

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

$\frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} - \tan^{2} (x) = 0$

Step 2.1.4

Simplify.

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Step 2.1.4.1

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

$\tan (x) \frac{\sin (x)}{\cos (x)} - \tan^{2} (x) = 0$

Step 2.1.4.2

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

$\tan (x) \tan (x) - \tan^{2} (x) = 0$

Step 2.1.4.3

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

$\tan^{1} (x) \tan (x) - \tan^{2} (x) = 0$

Step 2.1.4.4

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

$\tan^{1} (x) \tan^{1} (x) - \tan^{2} (x) = 0$

Step 2.1.4.5

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

${\tan (x)}^{1 + 1} - \tan^{2} (x) = 0$

Step 2.1.4.6

Add $1$ and $1$ .

$\tan^{2} (x) - \tan^{2} (x) = 0$

Step 2.2

Subtract $\tan^{2} (x)$ from $\tan^{2} (x)$ .

$0 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.