Find the exact value for the expression under the given conditions. tanα+β; cosα = −7/25 for α in Quadrant III and sinβ = −63/65 for β in Quadrant IV.

Answer 1

tan(α + β)= (tanα + tanβ)/(1 - tanαtanβ).

sinα = - √1 - 49/625 = - 24/25; tanα = sinα/cosα = 24/7;

cosβ = √1 - 3969/4225 = 16/65; tanβ = sinβ/cosβ = - 63/16;

tan(α + β) = (24/7 - 63/16)/(1 + 24/7·63/16) = - 57/1624