Trigonometry Examples

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

Step 1

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

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Step 1.1

Multiply by $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

$\sec^{2} (x) \sin^{2} (x)$

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

Step 4.2

One to any power is one.

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

Step 5

Combine $\frac{1}{\cos^{2} (x)}$ and $\sin^{2} (x)$ .

$\frac{\sin^{2} (x)}{\cos^{2} (x)}$

Step 6

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\tan^{2} (x)$