Trigonometry Examples

$\cos (4 x - 6) = \frac{1}{\sec (2 x + 14)}$

Step 1

Simplify $\frac{1}{\sec (2 x + 14)}$ .

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Step 1.1

Rewrite $\sec (2 x + 14)$ in terms of sines and cosines.

$\cos (4 x - 6) = \frac{1}{\frac{1}{\cos (2 x + 14)}}$

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (2 x + 14)}$ .

$\cos (4 x - 6) = 1 \cos (2 x + 14)$

Step 1.3

Multiply $\cos (2 x + 14)$ by $1$ .

$\cos (4 x - 6) = \cos (2 x + 14)$

Step 2

For the two functions to be equal, the arguments of each must be equal.

$4 x - 6 = 2 x + 14$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$4 x - 6 - 2 x = 14$

Step 3.2

Subtract $2 x$ from $4 x$ .

$2 x - 6 = 14$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $6$ to both sides of the equation.

$2 x = 14 + 6$

Step 4.2

Add $14$ and $6$ .

$2 x = 20$

Step 5

Divide each term in $2 x = 20$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 20$ by $2$ .

$\frac{2 x}{2} = \frac{20}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{20}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $20$ by $2$ .

$x = 10$