Умножаем все на √3
sin 2x + √3*cos 2x <= √3
2sin x*cos x + √3cos^2 x - √3*sin^2 x <= √3*cos^2 x + √3*sin^2 x
2sin x*cos x - 2√3*sin^2 x <= 0
2sin x*(cos x - √3*sin x) <= 0
1) sin x = 0; x1 = pi*n
2) √3*sin x = cos x
tg x = 1/√3; x2 = pi/6 + pi*n
Ответ: С) pi/6 + pi*n <= x <= pi + pi*n
8.
<u>x+4</u> - <u>3x-1</u> ≤ 2(x-1)
5 2
<u>x+4 </u> - <u>3x - 1</u> - 2x + 2 ≤0
5 2
Общий знаменатель: 5*2=10
2(x+4) -5(3x-1) -2x*10 +2*10 ≤ 0
2x+8-15x+5-20x+20 ≤0
-33x +33 ≤ 0
-33x ≤ -33
x≥ 1
x∈[1; +∞)
Ответ: 3)
1- а; 8 - б;
2- б; 9 - б;
3- б; 10 - а;
4- а; 11- в;
5- в; 12- б;
6- г; 13 - б
7-
Π=180°
1°=π/180°
1) 40 = 40°π/180° = 2π/9
2) 120° = 120°π/180° = 2π/3
3) 150° = 150°π/180° = 5π/6
4) 75° = 75°π/180° = 5π/12
5) 32° = 32°π/180° = 8π/45
6) 140° = 140°π/180° = 7π/9