find exact value using sum or differnce equations. tan(19pi/12)

Answer 1

Sometimes students find it easier to think in degrees
19π/12 radians = 285°

skipping the degree symbol ...
and 285 = 240+45
we know tan 240 = +tan60 = √3 by the CAST rule
tan 45 = 1

tan(285)
= tan(240 + 45)
= (tan240 + tan45)/(1 - tan240tan45)
= (√3+1)/(1-√3)

tan(19π/12) = (√3+1)/(1-√3)