Precalculus Examples

$\sin^{4} (0) - \cos^{4} (0) = 2 \sin^{2} (0) - 1$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\sin (0)$ is $0$ .

$0^{4} - \cos^{4} (0) = 2 \sin^{2} (0) - 1$

Step 1.2

Raising $0$ to any positive power yields $0$ .

$0 - \cos^{4} (0) = 2 \sin^{2} (0) - 1$

Step 1.3

The exact value of $\cos (0)$ is $1$ .

$0 - 1^{4} = 2 \sin^{2} (0) - 1$

Step 1.4

One to any power is one.

$0 - 1 \cdot 1 = 2 \sin^{2} (0) - 1$

Step 1.5

Multiply $- 1$ by $1$ .

$0 - 1 = 2 \sin^{2} (0) - 1$

Step 2

Subtract $1$ from $0$ .

$- 1 = 2 \sin^{2} (0) - 1$

Step 3

Simplify each term.

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Step 3.1

The exact value of $\sin (0)$ is $0$ .

$- 1 = 2 \cdot 0^{2} - 1$

Step 3.2

Raising $0$ to any positive power yields $0$ .

$- 1 = 2 \cdot 0 - 1$

Step 3.3

Multiply $2$ by $0$ .

$- 1 = 0 - 1$

Step 4

Subtract $1$ from $0$ .

$- 1 = - 1$

Step 5

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

$\sin^{4} (0) - \cos^{4} (0) = 2 \sin^{2} (0) - 1$ is an identity.