Algebra Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

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

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

Step 5

Cancel the common factor of $\cos^{2} (x)$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\sin^{2} (x)$