Precalculus Examples

$\frac{\sin (x)}{\sec (x)} - \frac{\sin (x) - 1}{\sec (x)}$

Step 1

Combine the numerators over the common denominator.

$\frac{\sin (x) - (\sin (x) - 1)}{\sec (x)}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{\sin (x) - \sin (x) - - 1}{\sec (x)}$

Step 2.2

Multiply $- 1$ by $- 1$ .

$\frac{\sin (x) - \sin (x) + 1}{\sec (x)}$

Step 3

Simplify by adding terms.

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Step 3.1

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

$\frac{0 + 1}{\sec (x)}$

Step 3.2

Add $0$ and $1$ .

$\frac{1}{\sec (x)}$

Step 4

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

$\frac{1}{\frac{1}{\cos (x)}}$

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

$1 \cos (x)$

Step 6

Multiply $\cos (x)$ by $1$ .

$\cos (x)$