Precalculus Examples

$x = x \cos (x) + y \sin (x)$

Step 1

Divide each term in the equation by $\cos (x)$ .

$\frac{x}{\cos (x)} = \frac{x \cos (x)}{\cos (x)} + \frac{y \sin (x)}{\cos (x)}$

Step 2

Separate fractions.

$\frac{x}{1} \cdot \frac{1}{\cos (x)} = \frac{x \cos (x)}{\cos (x)} + \frac{y \sin (x)}{\cos (x)}$

Step 3

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{x}{1} \cdot \sec (x) = \frac{x \cos (x)}{\cos (x)} + \frac{y \sin (x)}{\cos (x)}$

Step 4

Divide $x$ by $1$ .

$x \sec (x) = \frac{x \cos (x)}{\cos (x)} + \frac{y \sin (x)}{\cos (x)}$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Cancel the common factor.

$x \sec (x) = \frac{x \cos (x)}{\cos (x)} + \frac{y \sin (x)}{\cos (x)}$

Step 5.1.2

Divide $x$ by $1$ .

$x \sec (x) = x + \frac{y \sin (x)}{\cos (x)}$

Step 5.2

Separate fractions.

$x \sec (x) = x + \frac{y}{1} \cdot \frac{\sin (x)}{\cos (x)}$

Step 5.3

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

$x \sec (x) = x + \frac{y}{1} \cdot \tan (x)$

Step 5.4

Divide $y$ by $1$ .

$x \sec (x) = x + y \tan (x)$