Trigonometry Examples

$\tan (6 x) = \frac{1}{\cot (2 x + 4)}$

Step 1

Simplify $\frac{1}{\cot (2 x + 4)}$ .

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Step 1.1

Rewrite $\cot (2 x + 4)$ in terms of sines and cosines.

$\tan (6 x) = \frac{1}{\frac{\cos (2 x + 4)}{\sin (2 x + 4)}}$

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (2 x + 4)}{\sin (2 x + 4)}$ .

$\tan (6 x) = \frac{\sin (2 x + 4)}{\cos (2 x + 4)}$

Step 1.3

Convert from $\frac{\sin (2 x + 4)}{\cos (2 x + 4)}$ to $\tan (2 x + 4)$ .

$\tan (6 x) = \tan (2 x + 4)$

Step 2

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

$6 x = 2 x + 4$

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.

$6 x - 2 x = 4$

Step 3.2

Subtract $2 x$ from $6 x$ .

$4 x = 4$

Step 4

Divide each term in $4 x = 4$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $4$ by $4$ .

$x = 1$