Question

If `(1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@)) = 2kcos40^(@)`, then `18k^(4) + 162k^(2) + 369` is divisible by (A) `345` (B) `349` (C) `347` (D) `5`
A. `345`
B. `349`
C. `347`
D. `5`

Answer 1

Correct Answer - B::D
`2k cos40^(@) = (1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@))`
`= (sqrt(3)cos20^(@) + sin20^(@))/(sqrt(3)sin20^(@)cos20^(@))`
`= ((sqrt(3))/(2)cos20^(@) + (1)/(2)sin20^(@))/(sqrt(3)/(4)sin40^(@)) = (8cos40)/(sqrt(3))`
`3k^(2) = 16` so `18k^(4) + 162k^(2) + 369 = 1745`