Algebra Examples

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

Step 1

Divide each term in $- \sec^{2} (x) = 0$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \sec^{2} (x) = 0$ by $- 1$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2

Divide $\sec^{2} (x)$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $- 1$ .

$\sec^{2} (x) = 0$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$\sec (x) = \pm \sqrt{0}$

Step 3

Simplify $\pm \sqrt{0}$ .

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Step 3.1

Rewrite $0$ as $0^{2}$ .

$\sec (x) = \pm \sqrt{0^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$\sec (x) = \pm 0$

Step 3.3

Plus or minus $0$ is $0$ .

$\sec (x) = 0$

Step 4

The range of secant is $y \leq - 1$ and $y \geq 1$ . Since $0$ does not fall in this range, there is no solution.

No solution