Trigonometry Examples

$\tan^{2} (x) + 6 = \sec^{2} (x) + 5$

Step 1

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

$(\sec^{2} (x) - 1) + 6 = \sec^{2} (x) + 5$

Step 2

Add $- 1$ and $6$ .

$\sec^{2} (x) + 5 = \sec^{2} (x) + 5$

Step 3

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

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Step 3.1

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

$\sec^{2} (x) + 5 - \sec^{2} (x) = 5$

Step 3.2

Combine the opposite terms in $\sec^{2} (x) + 5 - \sec^{2} (x)$ .

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Step 3.2.1

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

$0 + 5 = 5$

Step 3.2.2

Add $0$ and $5$ .

$5 = 5$

Step 4

Since $5 = 5$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$