Trigonometry Examples

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

Step 1

Simplify $\sec^{2} (x) + \cos^{2} (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $\sec (x)$ in terms of sines and cosines.

${(\frac{1}{\cos (x)})}^{2} + \cos^{2} (x) = 0$

Step 1.1.2

Apply the product rule to $\frac{1}{\cos (x)}$ .

$\frac{1^{2}}{\cos^{2} (x)} + \cos^{2} (x) = 0$

Step 1.1.3

One to any power is one.

$\frac{1}{\cos^{2} (x)} + \cos^{2} (x) = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\cos^{2} (x)} + \cos^{2} (x) = 0$

Step 1.2.2

Rewrite $\frac{1^{2}}{\cos^{2} (x)}$ as ${(\frac{1}{\cos (x)})}^{2}$ .

${(\frac{1}{\cos (x)})}^{2} + \cos^{2} (x) = 0$

Step 1.2.3

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution