1) tg390° + cos840°- ctg135° + sin(-420°) =
= tg(390° - 360°) + cos(840°- 720°)- ctg (180°- 45°) - sin(420°- 360°) =
= tg 30° + cos 120°+ ctg 45° - sin 60° =
=√3/3 + cos (180° - 60°) + 1 - √3/2 =
=√3/3 - cos 60° + 1 - √3/2 =
=√3/3 - 1/2 + 1 - √3/2 =
= 1/2 - √3/6
2) cos 165° - tg75° =
= cos (90° + 75°) - tg75° =
= -sin 75° - sin 75°/cos75° =
= (-sin 75° · cos75° - sin 75°)/cos75° =
= (-0.5 sin 150° - sin 75°)/cos75° =
= (-0.5 sin (180°-30°) - sin (45°+30°)/cos(45°+30°) =
= (-0.5 sin 30° - sin 45°·cos30° - cos45°·sin30°)/(cos45°·cos 30°- sin45°·sin30°) =
= (-0.5 ·0.5 - 0.5√2 · 0.5√3 - 0.5√2 ·0.5)/(0.5√2·0.5√3- 0.5√2·0.5) =
= (-0.25 - 0.25√6 - 0.25√2 )/(0.25√6- 0.25√2) =
= -(1 + √6 + √2 )/(√6- √2) =
= -[(√6 + √2) + (√6 + √2)²]/(6- 2) =
= -[(√6 + √2) + (6 + 4√12 + 2)]/4 =
= -[√6 + √2 + 8 + 8√3]/4=
= -[√2(√3 +1) + 8(1 + √3]/4=
= -0.25[(√3 +1)(√2 + 8)]
3) sinx= - 0.5
x = -150°; -30°, 210°, 330°