The value of `[100(x-1)]` is where [X] is the greatest Integer less than or equal to `x` and `x=(sum_(n=1)^(44^(@))cosn^(@))/(sum_(n=1)^(44^(@))sinn^(@))`

Answer

2

Explanation

`x=(underset(n=1)overset(44)(.sum)cosn^(0))/(underset(n=1)overset(44)(.sum)sinn^(0))=(cos1^(0)+cos2^(0)+"...."cos44^(0))/(sin1^(0)+sin2^(0)+"...."sin44^(0))`
`((sin((44)/(2))^(0))/(sin((1)/(2))^(0))cos((1^(0)+44^(0))/(2)))/((sin((44)/(2))^(0))/(sin((1)/(2))^(0))sin((1^(0)+44^(0))/(2)))`
`rArr cot((45^(@))/(2))rArr cot(22(1^(@))/(2))`
`rArr x=(sqrt2+1)=2.414`