cos²(π/8) - sin²(π/8)
Using the trigonometric identity cos²(x) - sin²(x) = cos(2x):
cos(2 * π/8)
cos(π/4)
Since cos(π/4) = √2 / 2:
√2 / 2
cos²(π/8) - sin²(π/8)
Using the trigonometric identity cos²(x) - sin²(x) = cos(2x):
cos(2 * π/8)
cos(π/4)
Since cos(π/4) = √2 / 2:
√2 / 2