Which if the following is one of the goals for healthy people initiative? a. to eliminate all disease b. to eliminate health disparities among americans c. to eliminate quality and years of healthy life d. both b and c

Correct  cos(α - β) = 140/221

Step-by-step explanation:

cosα = ±√(1 - sin²α) => cosα = ±√(1 - (-5/13)²) = ±√(1 - (25/169)  

cosα = ±√(169 -25)/169 = ± √144/169

cosα = ± 12/13  since it is given that α (alpha) ends in the third quadrant

we choose  cosα = - 12/13

we know that is  tanβ = sinβ/cosβ = - 8/15 or sinβ : cosβ = 8 : 15 =>

sinβ = 8k and cosβ = 15k  where k is the coefficient of proportionality

we know the basic trigonometric equality

sin²β + cos²β = 1    when we replace the coefficients we get

(8k)² + (15k)² = 1 => 64k² + 225k² = 1 => 289k² = 1 => k² = 1/289 =>

k = 1/17   now we get sinβ and cosβ

since it is given that  β (beta) ends in the second quadrant

sinβ = 8/17 and cosβ = - 15/17

As we know it is:

cos(α - β) = cosα cosβ + sinα sinβ = - 12/13 · (- 15/17) + (- 5/13) · 8/17 =>

cos(α - β) = 180/221 - 40/221 = 140/221

cos(α - β) = 140/221

God is with you!!!