Trigonometry Examples

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

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

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

$\sec (x) = 0$

Step 2

Set $\sec^{2} (x + 2)$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $\sec^{2} (x + 2)$ equal to $0$ .

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

Step 2.2

Solve $\sec^{2} (x + 2) = 0$ for $x$ .

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Step 2.2.1

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

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

Step 2.2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

$\sec (x + 2) = \pm 0$

Step 2.2.2.3

Plus or minus $0$ is $0$ .

$\sec (x + 2) = 0$

Step 2.2.3

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

Step 3

The final solution is all the values that make $\sec^{2} (x + 2) \sec (x) = 0$ true.

No solution