1/3 V 45 = V ( 1/9 • 45 ) = V 5
1.
1)sin765=sin(720+45)=sin45=√2/2
2)cos19π/6=cos(3π+π/6)=cos(π+π/6)=-cosπ/6=-√3/2
2.
cosa=-√1-0,09=-√0,91=-0,1√91
3.
1)cosacosb+sinasinb-cosacosb+sinasinb=2sinasinb
2)(-sina-cosa)/(-2cosacosa+1)=-(sina+cosa)/(-2cos²a+sin²a+cos²a)=-(sina+cosa)/(sin²a-cos²a)=-(sina+cos)/(sina-cosa)(sina+cosa)=-1/(sina-cosa)=1/(cosa-sina)
4.sinxcos3x+cosxsin3x=-1
sin(x+3x)=-1
sin4x=-1
4x=-π/2+2πn
x=-π/8+πn/2
5.((sina/cosa+cosa/sina)*(cos²2a+sin²2a-cos²2a+sin²2a)= ((sin²a+cos²a)/sinacosa)*2sin²2a=2/sin2a*2sin²2a=4sin2a
Y=x^2 y=x+2 x=2 . y=2^2=4 . y=2+2=4
1/3( Х + у ) - 1/4( Х - у ) = 5
1/12( Х + у ) + 1/3( Х - у ) = 6
------
Х + у = а
Х - у = b
1/3a - 1/4b = 5
1/12a + 1/3b = 6
------
4a - 3b = 60
a + 4b = 72
- 4a - 16b = - 288
- 19b = - 228
b = 12
a + 48 = 72
a = 24
----
x + y = 24
x - y = 12
2x = 36
X = 18
y = 24 - 18
y = 6
ОТВЕТ ( 18 ; 6 )
Проверка :
1/3•( 18 + 6 ) - 1/4•( 18 - 6 ) = 5
1/12•( 18 + 6 ) + 1/3•( 18 - 6 ) = 6
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1/3•24 - 1/4•12 = 5
1/12•24 + 1/3•12 = 6
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8 - 3 = 5
2 + 4 = 6
------
5 = 5
6 = 6
∫(5+х)/(3x^2+1)dx
∫(x/3x²+1)+(56/3x²+1)dx={u=3x²+1; du=6xdx;dx=du/6x}=1/6∫du/u+5∫dx/(3x²+1)=
=logu/6+{s=√3dx}=logu/6+5/√3∫ds/(s²+1)=5tg⁻¹(s)/√3+logu/6=
=1/6log(3x²+1)+5tg⁻¹(√3x)/√3+c
