Answer:
-120/119
Step-by-step explanation:
cos α = -5/13 = adj/hyp
using Pythagoras theorem
hypotenuse ² = opposite² + adjacent ²
13² =opp²+ (-5)²
169 = opp² + 25
169-25 = 144 = opp²
opp = √144 = 12
sinα = opp/hyp = -12/13
sin β = -12/13
tan(α+β) = (tanα + tanβ)/ (1-tanαtanβ)
cos α = -5/13
sinα = 12/13
tanα= sinα/cosα = 12/13 / -5/13 = 12/-5 = -12/5
sin β = -12/13
cos β = 5/13
tan β = sinβ/cosβ = -12/13 / 5/13 = -12/5
tan(α+β) = (tanα + tanβ)/ (1-tanαtanβ)
tanα = -12/5
tanβ= -12/5
tan(α+β) = (tanα + tanβ)/ (1-tanαtanβ) = (-12/5+(-12/5))/(1-(-12/5)(-12/5))
(-12/5+(-12/5)) = -12-12/5 = -24/5
(1-(-12/5)(-12/5)) = 1-(144/25) = (25-144)/25 = 119/25
tan(α+β) = (tanα + tanβ)/ (1-tanαtanβ) = (-12/5+(-12/5))/(1-(-12/5)(-12/5)) =-24/5/119/25 = -24/5 x 25/119 = -24x5/119 = -120/119
