Which expression is equivalent to csc αcsc βcos(α+β) for all values of α and β for which csc αcsc βcos(α+β) is defined?

Question

select all that apply..

1+tan αtan β

cot αcot β−1

cot α+cot β

tan α−tan β

Answer 1

(cscα)(cscβ)cos(α+β) = (1/sinα)(1/sinβ)(cosαcosβ - sinαsinβ) =

(cosα/sinα)(cosβ/sinβ) - 1 = cotαcotβ - 1