Trigonometry Examples

$1 - \cos (12 x) = 2 \sin^{2} (6 x)$

Step 1

Subtract $2 \sin^{2} (6 x)$ from both sides of the equation.

$1 - \cos (12 x) - 2 \sin^{2} (6 x) = 0$

Step 2

Simplify $1 - \cos (12 x) - 2 \sin^{2} (6 x)$ .

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Step 2.1

Move $- 2 \sin^{2} (6 x)$ .

$1 - 2 \sin^{2} (6 x) - \cos (12 x) = 0$

Step 2.2

Apply the cosine double-angle identity.

$\cos (2 (6 x)) - \cos (12 x) = 0$

Step 2.3

Multiply $6$ by $2$ .

$\cos (12 x) - \cos (12 x) = 0$

Step 2.4

Subtract $\cos (12 x)$ from $\cos (12 x)$ .

$0 = 0$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$