Для начала найдем значения тригонометрических функций при соответствующих аргументах:

sin(-a) = -sin(a)
cos(0,5+a) = cos(0,5)cos(a) - sin(0,5)sin(a) = cos(0,5)cos(a) - sin(a)
ctg(pi/2+a) = 1/tg(pi/2+a) = 1/cot(a) = -tan(a)
tg(1,5pi-a) = -tan(a)

Теперь подставим значения в выражение:

(-sin(a)/(cos(0.5)cos(a) - sin(a))) - 2(-tan(a))(-tan(a))
(-sin(a)/(cos(0.5)cos(a) - sin(a))) + 2tan(a)tan(a)
(-sin(a)/cos(0.5)cos(a) - sin(a)) + 2tan^2(a)
(-sin(a)/cos(0.5)cos(a)) - (-sin(a)) + 2tan^2(a)
(-sin(a)/cos(0.5)cos(a) + sin(a)) + 2tan^2(a)
(sin(a)(1/cos(0.5)cos(a) + 1)) + 2tan^2(a)
(sin(a)(1/cos(0.5 + a)) + 2tan^2(a)
(sin(a)/cos(0.5 + a)) + 2tan^2(a)
tan(0.5 + a) + 2tan^2(a)
tan(0.5 + a) + 2tan^2(a)