Answer:
A
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1, hence
cos x = [tex]\sqrt{1-sin^2x}[/tex]
cosΘ = √(1 - ([tex]\frac{\sqrt{2} }{6}[/tex])²
= [tex]\sqrt{1-\frac{2}{36} }[/tex]
= [tex]\sqrt{1-\frac{1}{18} }[/tex] = [tex]\sqrt{\frac{17}{18} }[/tex] and
[tex]\sqrt{\frac{17}{18} }[/tex] = [tex]\frac{\sqrt{17} }{3\sqrt{2} }[/tex]
multiply numerator/ denominator by [tex]\sqrt{2}[/tex]
= [tex]\frac{\sqrt{34} }{6}[/tex] → A
