Trigonometry Examples

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

Step 1

Start on the left side.

$2 \cos^{2} (x) - 1$

Step 2

Apply Pythagorean identity in reverse.

$2 (1 - \sin^{2} (x)) - 1$

Step 3

Simplify.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$2 \cdot 1 + 2 (- {\sin (x)}^{2}) - 1$

Step 3.1.2

Multiply $2$ by $1$ .

$2 + 2 (- {\sin (x)}^{2}) - 1$

Step 3.1.3

Multiply $- 1$ by $2$ .

$2 - 2 {\sin (x)}^{2} - 1$

Step 3.2

Subtract $1$ from $2$ .

$- 2 \sin^{2} (x) + 1$

Step 4

Reorder terms.

$1 - 2 \sin^{2} (x)$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$2 \cos^{2} (x) - 1 = 1 - 2 \sin^{2} (x)$ is an identity