1) cosα · tgα - sinα = cosα · sinα/cosα - sinα = sinα - sinα = 0
2) cos2α - ? ctg2α - ? sinα = -2/3, 3π/2 < α < 2π - это IV четверть, где sinα < 0, cosα > 0.
cos2α = cos²α - sin²α = 1 - 2sin²α = 1 - 2 · (-2/3)² = 1 - 2 · 4/9 = 1 - 8/9 = 1/9
sin2α = 2sinα · cosα = 2 · (-2/3) · √5/3 = -4√5/9
cos²α = 1 - sin²α = 1 - (-2/3)² = 1 - 4/9 = 5/9; cosα = √(5/9) = √5/3
ctg2α = cos2α/sin2α = 1/9 : (-4√5/9) = -1/(4√5)
3) tg195° = tg(180° + 15°) = tg15° = tg(45° - 30°) =
= (tg45° - tg30°)/(1 + tg45° · tg30°) = (1 - √3/3)/(1 + 1 · √3/3) =
= (1 - √3/3)/(1 + √3/3) = (1 - √3/3)²/((1 + √3/3)(1 - √3/3)) =
= (1 + 3/9 - 2√3/3)/( 1 -3/9) = (1 + 1/3 - 2√3/3)/(1 - 1/3) = (4/3 -2√3/3)/(2/3) =
= (4 - 2√3)/3 : (2/3) = 2(2 - √3)/3 · 3/2 = 2 - √3
3(3x-1)>2(5x-7) 5(x+4)<2(4x-5) 2(x-7)-5x<_3x-11
9x-3>10x-14 5x+20<8x-10 2x-14-5x-3x+11<_0
9x-10x-3+14>0 5x-8x+20+10<0 -6x-3<_0
-x+11>0 -3x+30<0 -6x<_3
-x>-11 -3x<-30 x>_-0.5
x<11 x>10
(-бесконечность;11) (10;+бескон) [-0.5;+beskon)
2x+4(2x-3)>_12x-11 x-4(x-3)<3-6x
2x+8x-12-12x+11>_0 x-4x+12-3+6x<0
-2x-1>_0 3x+9<0
-2x>_1 3x<-9
x<_-0.5 x<-3
(-beskon;-0.5) (-beskon;-3)
vrode tak
