1) tg 85 + ctg 85 = tg(90-5) + ctg(90-5) = ctg 5 + tg 5 = = tg 5 + ctg 5 =
= sin 5/cos 5 + cos 5/sin 5 = (sin^2 5 + cos^2 5)/(sin 5*cos 5) =
= 1/(1/2*2sin 5*cos 5) = 2/sin 10
2) tg 15 + ctg 75 = tg 15 + ctg(90 - 15) = tg 15 + tg 15 = 2tg 15
3) sin 2x + cos 4x = sin 2x + 1 - 2sin^2 (2x) = -(2sin 2x + 1)(sin 2x - 1)