已知角a的终边经过点(cos5π/12-sin5π/12,cos5π/12+sin5π12)求tana

Question

已知角a的终边经过点(cos5π/12-sin5π/12,cos5π/12+sin5π12)求ta
na

Answer 1

已知角a的终边经过点P(cos5π/12-sin5π/12,cos5π/12+sin5π/12)
tana=(cos5π/12+sin5π/12)/(cos5π/12-sin5π/12)
tana=(1+tan5π/12)/(1-tan5π/12)
tan5π/12
=tan(2π/12+3π/12)
=tan(π/6+π/4)
=(tanπ/6+tanπ/4)/(1-tanπ/6*tanπ/4)
=(√3/3+1)/(1-√3/3*1)
=(3+√3)/(3-√3)
=(3+√3)^2/(3-√3)(3+√3)
=(9+2√3+3)/(9-3)
=(3+√3)/3
tana=(1+tan5π/12)/(1-tan5π/12)
=(1+ (3+√3)/3)/(1- (3+√3)/3)
=(3+3+√3)/(3-3-√3)
=(6+√3)/(-√3)
=-(1+2√3)