Trigonometry Examples

cos (3 x) = 4 {cos}^{3} (x) - 3 cos (x)

$\cos (3 x) = 4 \cos^{3} (x) - 3 \cos (x)$

Step 1

Apply the cosine triple-angle identity.

cos (3 x) = cos (3 x)

$\cos (3 x) = \cos (3 x)$

Step 2

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

3 x = 3 x

$3 x = 3 x$

Step 3

Move all terms containing

x

$x$ to the left side of the equation.

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Step 3.1

Subtract

3 x

$3 x$ from both sides of the equation.

3 x - 3 x = 0

$3 x - 3 x = 0$

Step 3.2

Subtract

3 x

$3 x$ from

3 x

$3 x$ .

0 = 0

$0 = 0$

0 = 0

$0 = 0$

Step 4

Since

0 = 0

$0 = 0$ , the equation will always be true for any value of

x

$x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$