Find the Exact Value 1-2sin(pi/8)^2

$1 - 2 \sin^{2} (\frac{π}{8})$

Apply the cosine double-angle identity.

$\cos (2 \frac{π}{8})$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\cos (2 \frac{π}{2 (4)})$

Cancel the common factor.

$\cos (2 \frac{π}{2 \cdot 4})$

Rewrite the expression.

$\cos (\frac{π}{4})$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{2}$

Decimal Form:

$0.70710678 \dots$