Find the exact value of tan(a+b) when cosa= 1/3 and sinb= -1/2

Answer 1

tan(a + b) = tan(a) + tab(b)

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1 - tan(a) tan(b)

use identity: cos^2 + sin^2 = 1

if cos(a) = 1/3, then (1/3)^2 + sin^2(a) = 1

sin^2(a) = 8/9

sin(a) = 2sqrt(2)/3

tan(a) = sin(a)/cos(a) = 2sqrt(2)

if sin(b) = -1/2, then cos(b)^2 + 1/4 = 1

cos(b)^2 = 3/4

cos(b) = sqrt(3)/2

tan(b) = sin(b)/cos(b) = -1/sqrt(3) = -sqrt(3)/3

plug tan(a) and tan(b) into formula.