s2x/c6x + s6x/c18x + s18x/c54x

2s2x.c2x/2c6x.c2x +..........................

s4x/2c6x.c2x+.....................

s(6-2)x/2c6x.c2x +.................

1/2[s6x.c2x - c6x.s2x]/c6x.c2x +.........

1/2[t6x-t2x] +............................

lll ly s6x/c18x =1/2[t18x-t6x] n s18x/c54x=1/2[t54x - t18x]

=> 1/2[t6x - t2x + t18x - t6x + t54x - t18x]

=>1/2[t54x- t2x]

thus the ans

 

3) a^2 + b^2=7(a+b)+ 102

  a+b=k k^2-7k-(102+2ab)=0

=>as k is real D >=0

 49+408 + 8 ab >=0

ab<=451/8

2 q) n2+3n+5=n+1)(n+2) + 3=0(mod11)

                      n+1)(n+2)=8(mod11)

  n+1)=1,2,4,8(mod11) (n+2)=1,2,4,8(mod11)

  n=0,12,,3,6,7,10(mod11)

hey the ans is this 2s2 +4s4+6s6+8s8..............172s172+176s176+178s178+180s180

s2=s178=>the expression is 180(s2+s4+s6+..s88)+90s90+(180s180=0)

180(s2+s4+s6.......s90)-90s90

sina +s(a+d)+s(a+2d)+.............s(a+n-1)d)=s[n.diff/2]/s[diff/2]*s[a+L/2]

=>180[s45/s1*s46]
i think nw u can do it