1) tg(45+a)*tg(45-a) = tg^2(45) - tg^2(a) = 1 - tg^2(a)
2) tg(a+60)tg(a-60) = tg(a+60)tg(60-a) = tg^2(60) - tg^2(a) = 3 - tg^2(a)
3) (1-tg(a))/(1+tg(a))-tg(45-a) = (1-tg^2(a))/(1+tg(a)) - tg(45-a) = (1-tg^2(a))/(1+tg(a)) - tg^2(45) + tg^2(a) = 1 - 2tg(a) - 1 + tg^2(a) + tg^2(a) = 2tg^2(a) - 2tg(a)
4) tg(45-a)-(1-tg(a))/(1+tg(a)) = tg^2(45) - tg^2(a) - (1-tg^2(a))/(1+tg(a)) = 1 - tg^2(a) - 1 - tg^2(a) = -2tg^2(a)
1) tg(45+a)*tg(45-a) = tg^2(45) - tg^2(a) = 1 - tg^2(a)
2) tg(a+60)tg(a-60) = tg(a+60)tg(60-a) = tg^2(60) - tg^2(a) = 3 - tg^2(a)
3) (1-tg(a))/(1+tg(a))-tg(45-a) = (1-tg^2(a))/(1+tg(a)) - tg(45-a) = (1-tg^2(a))/(1+tg(a)) - tg^2(45) + tg^2(a) = 1 - 2tg(a) - 1 + tg^2(a) + tg^2(a) = 2tg^2(a) - 2tg(a)
4) tg(45-a)-(1-tg(a))/(1+tg(a)) = tg^2(45) - tg^2(a) - (1-tg^2(a))/(1+tg(a)) = 1 - tg^2(a) - 1 - tg^2(a) = -2tg^2(a)