`int(cosec^2x-2005)/cos^[2005]x.dx`
`int(cosec^2x-2005)/cos^[2005]x.dx`
A. `(cotx)/((cosx)^(2005))+c`
B. `(tan x)/((cosx)^(2005))+c`
C. `(-(tan x))/((cosx)^(2005))+c`
D. none of these
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Correct Answer - D
`int("cosec"^(2)x-2005)/(cos^(2005)x)dx`
`=int(cotx)^(-2005)"cosec"^(2)xdx-2005 int (dx)/(cos^(2005)x)`
`=(cosx)^(-2005)(-cot x)-int (-2005)(cosx)^(-2006)(-sinx)(-cotx)dx-2005int(dx)/(cos^(2005)x)`
`= -(cotx)/((cosx)^(2005))+C`
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