Answer:
1, 0
Step-by-step explanation:
Let [tex]\cos (x+2\pi) = -\frac{\sqrt{2}}{2}[/tex]. From Trigonometry we remember the following identity:
[tex]\cos (a+b) = \cos a \cdot \cos b - \sin a \cdot \sin b[/tex] (Eq. 1)
Where [tex]a[/tex] and [tex]b[/tex] are angles measured in radians.
Then, we proceed to expand the given expression:
[tex]\cos x \cdot \cos 2\pi - \sin x \cdot \sin 2\pi = -\frac{\sqrt{2}}{2}[/tex]
[tex]\cos x \cdot 1 - \sin x \cdot 0 = -\frac{\sqrt{2}}{2}[/tex]
[tex]\cos x = -\frac{\sqrt{2}}{2}[/tex]
Therefore, correct answer is "1, 0".
