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Answer:
cos(-π/8) = (√(2+√2))/2
Step-by-step explanation:
The half-angle formula is ...
[tex]\cos{\dfrac{\theta}{2}}=\pm\sqrt{\dfrac{1+\cos{\theta}}{2}}[/tex]
Since cosine is an even function, cos(-π/8) = cos(π/8).
For θ/2 = π/8, θ = π/4 and cos(θ) = (√2)/2. Filling in the formula, we have ...
[tex]\cos{(-\dfrac{\pi}{8})}=\cos{\dfrac{\pi}{8}}=\sqrt{\dfrac{1+\cos{\dfrac{\pi}{4}}}{2}}=\sqrt{\dfrac{1+\dfrac{\sqrt{2}}{2}}{2}}\\\\=\sqrt{\dfrac{2+\sqrt{2}}{4}}=\boxed{\dfrac{\sqrt{2+\sqrt{2}}}{2}}[/tex]
