Evaluate cos(pi/4)^2-sin(pi/4)^2

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

Apply the cosine double-angle identity.

$\cos (2 \frac{π}{4})$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\cos (2 \frac{π}{2 (2)})$

Cancel the common factor.

$\cos (2 \frac{π}{2 \cdot 2})$

Rewrite the expression.

$\cos (\frac{π}{2})$

$\cos (\frac{π}{2})$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0$

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