Trigonometry Examples

$\frac{\sin (3 x)}{\sin (x)} = 2 \cos^{2} (x)$

Step 1

Subtract $2 \cos^{2} (x)$ from both sides of the equation.

$\frac{\sin (3 x)}{\sin (x)} - 2 \cos^{2} (x) = 0$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\frac{\sin (3 x)}{\sin (x)}$ as a product.

$\sin (3 x) \frac{1}{\sin (x)} - 2 \cos^{2} (x) = 0$

Step 2.2

Write $\sin (3 x)$ as a fraction with denominator $1$ .

$\frac{\sin (3 x)}{1} \cdot \frac{1}{\sin (x)} - 2 \cos^{2} (x) = 0$

Step 2.3

Simplify.

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Step 2.3.1

Divide $\sin (3 x)$ by $1$ .

$\sin (3 x) \frac{1}{\sin (x)} - 2 \cos^{2} (x) = 0$

Step 2.3.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\sin (3 x) \csc (x) - 2 \cos^{2} (x) = 0$

Step 3

Set the argument in $\csc (x)$ equal to $π n$ to find where the expression is undefined.

$x = π n$ , for any integer $n$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${x | x = π n}$ $n$ , for any integer $n$

Step 5