1) x+8<0<br>x<-8<br>2) cos2a + cos14a + cos6a + cos10a =
(cos14a + cos2a) + (cos10a + cos6a) =
(2 * cos((14a + 2a) / 2) * cos((14a - 2a) / 2)) +
(2 * cos((10a + 6a) / 2) * cos((10a - 6a) / 2)) =
2 * cos(8a) * cos(6a) +
2 * cos(8a) * cos(2a) = 2cos(8a) * (cos6a + cos2a) =
2cos(8a) * (2cos((6a+2a)/2)*cos((6a-2a)/2)) =
4cos(8a) * cos(4a) * cos(2a)
3) a2=a1+d
d=3-1=2
Sn = (a1+an) *n/2 = (1+x)*n/2 =625
1+x= 1250/n
n=1250/(1+x) = 1250 + 1250/x
2a1+d*(n-1)=1+x=1250/n
2+2*(n-1) = 1250/n
2+2n-2 =1250/n
2n=1250/n
3n=1250
n=416,6