Algebra Examples

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

Step 1

Replace the $\sec^{2} (x)$ with $1 + \tan^{2} (x)$ based on the $\tan^{2} (x) + 1 = \sec^{2} (x)$ identity.

$(1 + \tan^{2} (x)) - \tan^{2} (x) = 1$

Step 2

Combine the opposite terms in $1 + \tan^{2} (x) - \tan^{2} (x)$ .

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Step 2.1

Subtract $\tan^{2} (x)$ from $\tan^{2} (x)$ .

$1 + 0 = 1$

Step 2.2

Add $1$ and $0$ .

$1 = 1$

Step 3

The equation is always true.

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$