Evaluate the expression under the given conditions. cos (θ - ϕ); cos θ = 3 5, θ in quadrant iv, tan ϕ = - 15, ϕ in quadrant ii

Begin with cos (θ) = 5/13, θ in Quadrant IV

you should distinguish the 5-12-13 right-angled triangle

and then cosØ = adjacent/hypotenuse

x = 5, r = 13, y = - 12, since Ø is in IV

and sinØ = - 12/13

also tan (ϕ) = - √15 = - √15/1 = y/x and ϕ is in II,

y = √15, x = - 1

r^2 = x^2 + y^2 = 15+1 = 16

r = 4

sinϕ = √15/4, cosϕ = - 1/4

you must know that:

cos (θ - ϕ) = cosθcosϕ + sinθsinϕ

= (5/13) (-1/4) + (-12/13) (√15/4)

= - 5/52 - 12√15/52

= (-5-12√15) / 52