Algebra Examples

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

Step 1

Apply pythagorean identity.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

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

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

Step 5

Apply basic rules of exponents.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

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

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$1$