Trigonometry Examples

$1 - \frac{1}{\cos^{2} (x)}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $1$ as $1^{2}$ .

$1 - \frac{1^{2}}{\cos^{2} (x)}$

Step 1.1.2

Rewrite $\frac{1^{2}}{\cos^{2} (x)}$ as ${(\frac{1}{\cos (x)})}^{2}$ .

$1 - {(\frac{1}{\cos (x)})}^{2}$

Step 1.1.3

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

$1 - \sec^{2} (x)$

Step 1.2

Simplify with factoring out.

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Step 1.2.1

Reorder $1$ and $- \sec^{2} (x)$ .

$- \sec^{2} (x) + 1$

Step 1.2.2

Factor $- 1$ out of $- \sec^{2} (x)$ .

$- (\sec^{2} (x)) + 1$

Step 1.2.3

Rewrite $1$ as $- 1 (- 1)$ .

$- \sec^{2} (x) - 1 \cdot - 1$

Step 1.2.4

Factor $- 1$ out of $- \sec^{2} (x) - 1 \cdot - 1$ .

$- (\sec^{2} (x) - 1)$

Step 2

Apply pythagorean identity.

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