Tgx <= V3/3
Tgx = V3/3
x = pi/6 +pin Решением неравенства будет.
-pi/2 < x <= pi/6 + pin
Ответ. (-pi/2 + pin; pi/6 + pin], где n принадлежит Z
1) cos69=cos (90-21)=sin21;
cos79=sin11; cos10+cos11cos21+sin21sin11=cos10+cos (21-11)=2cos10;
2) sin20+sin13cos33-sin33cos13=sin20+sin (13-33)=0;
Sin 5x = 1 - 2Cos² 3x
Sin 5x = - Cos 6x
Sin 5x + Cos 6x = 0
Sin 5x + Sin(π/2 - 6x) = 0
2Sin(π/4 - х/2)Сos( 11x/2 - π/4) = 0
а) Sin (π/4 - х/2) = 0 или б) Cos(11x/2 - π/4) = 0
π/4 - х/2 = πn, n∈Z 11x/2 - π/4 = π/2 + πк, к ∈Z
-x/2 = πn + π/4, n ∈Z 11x/2 = π/2 + π/4 + πк, к∈Z
x = -2πn - π/2, n ∈Z x = 3π/22 + 2πк/11, к ∈Z
1. 7-1/243*x^3 x=-3
7-1/243*(-3)^3=7-(-(3^3)/3^5)=7+3^2=16
2. А) 4,9^8*(10/49)^8=4,9^8*10^8/49^8=49^8/49^8=1
Б) 64^5*8^12/(2^20*4^20)=2^30*2^36/(2^60)=2^6=64
3. А) (10/13)^0-6^2*1/64=1-2^2*3^2/2^6=1-9/16=7/16
Б)
4. А) (x^4)^5*x^8/x^24=x^4*5+8-24=x^4
Б) (a^8*a^7)^2:a^22=a^(8+7)*2-22=a^8