1)sin 45° + cos 135° - tg 60° = √2/2 + cos(180°-45°) - √3 = √2/2 - cos 45° - √3 = √2/2 - √2/2 - √3 = -√3

2)cos (3π/4) + sin (π/4) -3*sin (5π/6) + 4*tg (7π/4) = cos(π/2+π/4) + sin π/4 -3*sin(π/2+π/3) + 4*tg(3π/2+π/4) = - sin (π/4) + sin (π/4) + 3*cos (π/3) - 4*ctg (π/4) = 3*(1/2) - 4*1 = 1,5 - 4 = - 2,5

3) ctg² (5π/6) - 3*cos (2π/3) - 4*sin (5π/4) = ctg² (π/2+π/3) - 3*cos (π-π/3) - 4*sin (π/2+π/3) = - tg² (π/3) + 3*cos (π/3) - 4*cos (π/3) = - (√3)² + 3*(1/2) - 4*(1/2) = -3 +1,5 - 2 = -3,5

4)10*sin (-π/3) + 7*cos (-5π/6) - 3*tg(-5π/6) = 10*(-sin (π/3)) + 7*cos (π/2+π/3) - 3* (-tg (π/2+π/3)) = 10*(-√3/2) - 7*sin (π/3) + 3*(tg(π/2+π/3)) = -5√3 -7*(√3/2) +3*(-ctg (π/3)) = -5√3 -7√3/2 - 3/√3 = -10-14-6√3/2√3 = -6(4+√3)/2√3 = -√3(4+√3)/-4√3-3 = -(4√3+3)

5)12*sin (25π/6) +7*cos (22π/3) - 3*ctg (17π/4) = 12*sin (4π+π/6) + 7*cos (7π+π/3) - 3*ctg (4π + π/4) = 12*sin π/6 + 7*(-cos (π/3)) - 3*ctg (π/4) = 12*(1/2) + 7*(-1/2) - 3*1 = 6-3,5-3 = - 0,5

6)3*tg 405°-2*sin 780° + 2*cos 390° = 3*tg (360°+45°) - 2*sin (2*360°+60°) + 2*cos(360°+30°) = 3*tg 45° - 2*sin 60° + 2*cos 30° = 3*1 - 2*(√3/2) + 2*(√3/2) = 3