9x²-6x+1+16x²+40x+25-25x²+70x-49=0
104x=23
x=23/104
1) a+b+c
17+(-21)-(-14)=17-21+14=10
Ответ: 10
2) (14-с)+3d
(14-35)+3*(-11)=-21+(-33)=-21-33=-54
Ответ: -54
{2x+y=-1
{x+2y=2
x=2-2y
2(2-2y)+y=-1
4-4y+y=-1
-3y=-1-4
-3y=-5
y=<u>5 </u> = 1 ²/₃
3
x=2-2*<u> 5 </u>=2 - <u>10 </u>=<u> 6-10 </u>=<u> -4 </u>= -1 ¹/₃
3 3 3 3
Ответ: х= -1 ¹/₃
у= 1 ²/₃.
1. sin^2 x = 0,9
cos^2 x = 1 - sin^2 x = 1 - 0,9 = 0,1
11 - 99cos^2 x = 11 - 99*0,1 = 11 - 9,9 = 1,1
2. tg a = 2; 1/cos^2 a = 1 + tg^2 a = 1 + 4 = 5
cos^2 a = 1/5; sin^2 a = 1 - cos^2 a = 1 - 1/5 = 4/5
a ∈ [pi; 2pi], поэтому sin a < 0
sin a = -2/√5
sin a / (√5) = -(2/√5) / (√5) = -2/5
3. sin (33pi/4) = sin (32pi/4 + pi/4) = sin (pi/4) = √2/2
cos (34pi/3) = cos (30pi/3 + 4pi/3) = cos (4pi/3) = -cos (pi/3) = -1/2
√32*sin (33pi/4)*cos (34pi/3) = 4√2*√2/2*(-1/2) = -4/2*(√2*√2)/2 = -2
4. Формулы синуса и косинуса двойных углов:
sin 2a = 2sin a*cos a; cos 2a = 2cos^2 a - 1
Подставляем в пример
1 - 2cos^2 (111) = -cos (222) = -cos (180 + 42) = cos 42
cos^2 (114) = cos^2 (180 - 66) = (-cos 66)^2 = cos^2 (66)
10cos^2 (66)*tg (66) = 10cos^2 (66)*sin (66)/cos (66) =
= 10cos (66)*sin (66) = 5sin (132) = 5sin (90 + 42) = 5cos 42
Получаем
[1 - 2cos^2 (111)] / [10cos^2 (114)*tg (66)] = cos 42 / (5cos 42) = 1/5
Sin2x + cos2x = 1
tgx = sinx
cosx
ctgx = cosx
sinx
tgx ctgx = 1
tg2x + 1 = 1
cos2x
ctg2x + 1 = 1
sin2x
