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If (1)/(sin20^(@))+(1)/(sqrt(3)cos 20^(@...

If `(1)/(sin20^(@))+(1)/(sqrt(3)cos 20^(@))=2k cos 40^(@)`, then
`18k^(4)+162k^(2)+369` is equal to

A

`345`

B

`349`

C

`347`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
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`
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