5. cos(П/5+2П/15)= cos П/3= 1/2
6.sin( 3П/8-5П/24)= sin 4П/24= sin П/6= 1/2
8. tg(13+32)= tg 45=1
9.tg(65-35)= tg 30=√3/3
10. tg (111+24)= tg 135= -1
11. tg( 67+83)= tg 150= √3/3
12. sin (7+47)/sin (13+41)= sin 54/sin54=sin1=П/2
13. cos (51+12)/ sin (13+14)= cos 63/sin27= сtg 7/3
14. (cos(105-75)-cos(105+75))/2= (cos30-cos180)/2= ((√3/2)+1)/2
15.(sin(П/24+7П/24)+sin(7П/24-П/24))/2= (sin 8П/24+sin(6П/24))/2= (sinП/3+sin П/4)/2= ((√3/2)+(√2/2))/2
16. (cos240 + cos30)/2= (-1/2+ 1/2)/2=0
17.2 cos 60*cos 45= 2* (√3/2) * (√2/2)
5.2*1000-0.5*100=5200-50=5150
Cos^2x-cosx-2=0
обозн. cosx=t, |t|<=1
t2-t-2=0
d=(-1)^2-4*1*(-2)=1+8=9
t1=1-3/2 t2=1+3/2
t1=-1 t2=2
t2>1
cosx=-1
x=pi+2pi*n
2.2cos^2x-sin4x=1
2(1-sin^2x)-2sin2xcos2x=1
2-2sin^2x-2(2sinxcosx*(cos^2x-sin^2x)=1
2-2sin^2x-4sinxcosx(cos^2x-sin^2x)-1=0
(1-2sin^2x)-4sinxcosx(1-sin^2x-sin^2x)=0
(1-sin^2x)-4sinxcosx(1-2sin^2x)=0
(1-sin^2x)(1-4sinxcosx)=0
1-sin^2x=0 или 1-4sinxcosx=0
sin^2x=1/2 1-2sin2x=0
x=(-1)^n*arcsin(1/2)+pi*n sin2x=1/2
x=(-1)^n*pi/6+pi*n 2x=(-1)^n*arcsin(1/2)+pi*n
x=(-1)^n*pi/6+pi*n x=(-1)^n*pi/6+pi*n
<span> x=(-1)^n*pi/12+pi*n/2</span>
А2+а4=14
а7=а3+12
1)а1+д+а1+3д=14
2а1+4д=14
а1+2д=7
2)а7-а3=12
а1+6д-(а1+2д)=12
а1+6д-а1-2д=12
4д=12
д=3
3)а1+6=7
а1=1