simplify tan(-17 degree)+sin(24 degree)+cot(73 degrees)+cos(66 degrees in(-24 degree)

You will have to know the co-function properties

notice that the 6 trig names come as
sine vs cosine
tan vs cotan
sec vs cosecant

we need only the first two
sinx = cos(90-x)
tanx = cot(90-x)

secondly we have to know
tan(-x) = -tanx and sin(-x) = -sinx

tan(-17°) + sin24° + cot73° + cos66° + sin(-24°)
I assumed your last term, as you had a typo

= -tan17 + sin24 + tan17 + cos66 - sin24
= cos 66°