Trigonometry Examples

$\cos^{2} (2 u) - \sin^{2} (2 u) = \cos (4 u)$

Step 1

Subtract $\cos (4 u)$ from both sides of the equation.

$\cos^{2} (2 u) - \sin^{2} (2 u) - \cos (4 u) = 0$

Step 2

Simplify $\cos^{2} (2 u) - \sin^{2} (2 u) - \cos (4 u)$ .

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Step 2.1

Apply the cosine double-angle identity.

$\cos (2 (2 u)) - \cos (4 u) = 0$

Step 2.2

Multiply $2$ by $2$ .

$\cos (4 u) - \cos (4 u) = 0$

Step 2.3

Subtract $\cos (4 u)$ from $\cos (4 u)$ .

$0 = 0$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$