Find the exact value for the expression under the given conditions. Write your answer in simplest form. (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 - (-7/25)² = - 24/25; tanα = 24/7; cosβ = √1 - (- 63/65)² = 16/65; tanβ = - 63/16.

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