a) cos(-a) - cos(π - a)
= cos(a) + cos(a)
= 2cos(a)

b) sin(90° - a) - cos(180° - a) + tg(180 - a) - ctg(270° + a)
= cos(a) - cos(a) + (-cot(a)) - tan(a)
= -2cos(a) - 2cot(a)

c) cos(100°) + sin(530°)
= cos(100°) + sin(170°)
= cos(100°) + sin(10°)
= cos(10°) + sin(10°)
= √2 * sin(45°)
= √2 / 2

d) 3tg(930°) + sin(1200°) - cos(1410°)
= 3tan(210°) + sin(360°) - cos(90°)
= 3(-√3) + 0 - 0
= -3√3

e) sin(-13π/6) + cos(17π/3) + tg(22π/3) - ctg(37π/4)
= -sin(π/6) + cos(π/3) + tan(2π/3) - 1
= -1/2 + 1/2 + √3 - 1
= √3 - 1

f) sin(3π/2 - a/2) / cos(3π/2 - a/2)
= sin(π + π/2 - a/2) / cos(π + π/2 - a/2)
= sin(π/2 - a/2) / cos(π/2 - a/2)
= cos(a/2) / sin(a/2)
= tg(a/2)