Find the exact value of tanalpha beta for cos alpha 12 pi2

Find the exact value of tan(alpha - beta) for cos alpha = 1/2, pi/2

Solution

cos =1/2 ,-/2 <<0

=> =-/3

tan =tan(-/3) =-3

sin =1/3 ,0< </2

=>tan=1/((3²-1²))

tan =1/8

tan(-)= (tan -tan)_{/(1+ tantan)}

tan(-)= (-(3) -(1/8))_{/(1+ (-3)(1/8))}

tan(-)= (-(24) -1)_/(8-3)