Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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