Tangent Addition Formula

Question

If tanα =  and tanβ = , then tan(α - β) = _____.

-2

-2

-

Answer 1

tan (a-b) = (tan A - tan B)/(1 + tanA tanB)

= (1/2 - 4/3) / ( 1 + (1/2)(4/3))

= (1/2 - 4/3) / ( 1 + 2/3)

= (-5/6) / (5/3)

= -5/6 * 3/5 = -1/2