Suppose cot alpha=-3/2 and cot beta=-4 where pi/2<alpha<beta<pi. Find tan(alpha-beta).

Question

Simplify the expression

Answer 1

cot alpha=-3/2

cosα/sinα=-1.5

α=-33.7°or 146.3°

cosβ/sinβ=-4

β=-14°or 166°

146.3-166=-19.7tan=-358.051°

Answer 2

tan(α - β) =(tanα - tanβ)/(1 + tanαtanβ); tanα = 1/cotα = - 2/3, tanβ = - 1/4.

So, tan(α - β) = (- 2/3 + 1/4)/(1 + 2/3·1/4) = (- 5/12)/(7/6) = - 5/14

Answer 3

cot α = -3/2 ⇒ tan α = -2/3

cot β = -4 ⇒ tan β = -1/4

Substitute values in sum formula and simplify