10-2

Sum formula for tangent: tan(α + β) = tanα + tanβ/1 – tanαtanβ

Difference formula for tangent: tan(α – β) = tanα - tanβ/1 + tanαtanβ

Ex 1. Suppose tanα = 1/3 and tanβ = ½

a. Find tan(α + β)

tanα + tanβ/1 – tanαtanβ

1/3 + ½ / 1 – (1/3)(1/2)

2/6 + 3/6 / 1 – 1/6

5/6 / 5/6 = 1

b. Find tan(α – β)

tanα - tanβ/1 + tanαtanβ

1/3 – ½ / 1 + (1/3)(1/2)

2/6 - 3/6 / 1 + 1/6

-1/6 / 7/6 = -6/42 = -1/7