Trigonometry Examples

$\cos (x) + 10 \sec (x) = 7$

Step 1

Simplify $\cos (x) + 10 \sec (x)$ .

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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.

$\cos (x) + 10 \frac{1}{\cos (x)} = 7$

Step 1.1.2

Combine $10$ and $\frac{1}{\cos (x)}$ .

$\cos (x) + \frac{10}{\cos (x)} = 7$

Step 1.2

Simplify each term.

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Step 1.2.1

Separate fractions.

$\cos (x) + \frac{10}{1} \cdot \frac{1}{\cos (x)} = 7$

Step 1.2.2

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

$\cos (x) + \frac{10}{1} \sec (x) = 7$

Step 1.2.3

Divide $10$ by $1$ .

$\cos (x) + 10 \sec (x) = 7$

Step 2

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

No solution