Algebra Examples

{cos}^{2} (\frac{π}{4}) - {sin}^{2} (\frac{π}{4})

$\cos^{2} (\frac{π}{4}) - \sin^{2} (\frac{π}{4})$

Step 1

Apply the cosine double-angle identity.

cos (2 \frac{π}{4})

$\cos (2 \frac{π}{4})$

Step 2

Cancel the common factor of

2

$2$ .

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Step 2.1

Factor

2

$2$ out of

4

$4$ .

cos (2 \frac{π}{2 (2)})

$\cos (2 \frac{π}{2 (2)})$

Step 2.2

Cancel the common factor.

$\cos (2 \frac{π}{2 \cdot 2})$

Step 2.3

Rewrite the expression.

$\cos (\frac{π}{2})$

$\cos (\frac{π}{2})$

Step 3

The exact value of

$\cos (\frac{π}{2})$ is

$0$ .

$0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$