Trigonometry Examples

$\frac{\sec (x)}{\tan (x)} = \csc (x)$

Step 1

Subtract $\csc (x)$ from both sides of the equation.

$\frac{\sec (x)}{\tan (x)} - \csc (x) = 0$

Step 2

Simplify $\frac{\sec (x)}{\tan (x)} - \csc (x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{\sec (x)}{\frac{\sin (x)}{\cos (x)}} - \csc (x) = 0$

Step 2.1.2

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

$\frac{\frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} - \csc (x) = 0$

Step 2.1.3

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

$\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \csc (x) = 0$

Step 2.1.4

Cancel the common factor of $\cos (x)$ .

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Step 2.1.4.1

Cancel the common factor.

$\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \csc (x) = 0$

Step 2.1.4.2

Rewrite the expression.

$\frac{1}{\sin (x)} - \csc (x) = 0$

Step 2.1.5

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x) - \csc (x) = 0$

Step 2.2

Subtract $\csc (x)$ from $\csc (x)$ .

$0 = 0$

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.