Trigonometry Examples

$\frac{- 4 \tan^{2} (t) - 4}{\sec^{2} (t)}$

Step 1

Factor $4$ out of $- 4 \tan^{2} (t) - 4$ .

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Step 1.1

Factor $4$ out of $- 4 \tan^{2} (t)$ .

$\frac{4 (- \tan^{2} (t)) - 4}{\sec^{2} (t)}$

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{4 (- \tan^{2} (t)) + 4 (- 1)}{\sec^{2} (t)}$

Step 1.3

Factor $4$ out of $4 (- \tan^{2} (t)) + 4 (- 1)$ .

$\frac{4 (- \tan^{2} (t) - 1)}{\sec^{2} (t)}$

Step 2

Factor $- 1$ out of $- \tan^{2} (t)$ .

$\frac{4 (- (\tan^{2} (t)) - 1)}{\sec^{2} (t)}$

Step 3

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

$\frac{4 (- (\tan^{2} (t)) - 1 (1))}{\sec^{2} (t)}$

Step 4

Factor $- 1$ out of $- (\tan^{2} (t)) - 1 (1)$ .

$\frac{4 (- (\tan^{2} (t) + 1))}{\sec^{2} (t)}$

Step 5

Simplify the expression.

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Step 5.1

Rewrite $- (\tan^{2} (t) + 1)$ as $- 1 (\tan^{2} (t) + 1)$ .

$\frac{4 (- 1 (\tan^{2} (t) + 1))}{\sec^{2} (t)}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{4 (\tan^{2} (t) + 1)}{\sec^{2} (t)}$