The integer part of the number
`sum_(k=0)^(44)(1)/(cos(k)^(@)cos(k+1)^(@))` is

Options

A. 50
B. 52
C. 57
D. 59

Answer

C

Explanation

`(1)/(cos0^(@) cos 1^(@))+(1)/(cos 1^(@)cos2^(@))+(1)/(cos2^(@) cos3^(@))+.......(1)/(cos 44^(@) cos 45^(@))`
multiply & divided by `sin 1 ^(@)`
`(1)/(sin1^(@))[(sin1^(@))/(cos0^(@) cos 1^(@))+(sin1^(@))/(cos 1^(@)cos2^(@))+.......(sin1^(@))/(cos 44^(@) cos 45^(@))]`
`(1)/(sin1^(@))[(sin(1^(@)-0^(@)))/(cos0^(@) cos 1^(@))+(sin(1^(@)-0^(@)))/(cos 1^(@)cos2^(@))+.......sin(1^(@)-0^(@))/(cos 44^(@) cos 45^(@))]`
`(1)/(sin 1^(@))[tan1^(@)-tan0^(@)+tan2^(@)-tan1^(@)+...tan45^(@)-tan44^(@)]`
`=(1)/(sin 1^(@))[tan 45^(@)]`
`(1)/(0.0174524)=57.2987`
Integral part = 57