The greatest integer less than or equal to `1/(cos290^0)+1/(sqrt(3)sin250^0)` is _____

Answer

2

Explanation

`cos 290^(@) = sin 20^(@) , sin 250^(@) = - sin 70^(@) =-cos 20^(@)`
`rArr (1)/( sin 20^(@)) - (1)/(sqrt3 cos 20^(@))`
`" " = (sqrt3 cos 20^(@) - sin 20^(@))/(sqrt3 sin 20^(@) cos 20^(@))`
`" " =(2 [sin 60^(@) cos 20^(@) - sin 20^(@)cos 60^(@)])/(sqrt3 sin 20^(@) cos 20^(@))`
`= (4 sin 40^(@))/(sqrt3 sin 40^(@)) = (4sqrt3)/(3)`
Hence, the greatest integer less than or equal to is 2.