Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factors.

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

Step 1.2

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

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

Step 1.3

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

$1 + \cos (x) - (1 \cos (x))$

Step 1.4

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

$1 + \cos (x) - \cos (x)$

Step 2

Combine the opposite terms in $1 + \cos (x) - \cos (x)$ .

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Step 2.1

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

$1 + 0$

Step 2.2

Add $1$ and $0$ .

$1$