Precalculus Examples

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

Step 1

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

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

Step 2

Subtract $2$ from $1$ .

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

Step 3

Move all terms containing $\tan (x)$ to the left side of the equation.

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Step 3.1

Subtract $\tan^{2} (x)$ from both sides of the equation.

$\tan^{2} (x) - 1 - \tan^{2} (x) = 0$

Step 3.2

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

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Step 3.2.1

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

$0 - 1 = 0$

Step 3.2.2

Subtract $1$ from $0$ .

$- 1 = 0$

Step 4

Since $- 1 \neq 0$ , there are no solutions.

No solution