Answer: [tex]\bold{-\dfrac{161}{289}}[/tex]
Step-by-step explanation:
Given: cos x = [tex]\dfrac{8}{17}[/tex], x is in Quadrant 4
Use Pythagorean Theorem to find sin x:
8² + y² = 17²
y² = 17² - 8²
y² = 289 - 64
y² = 225
y = 15
→ sin x = [tex]-\dfrac{15}{17}[/tex]
Use the double angle formula to find cos (2x):
[tex]cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}[/tex]
