The minimum value of the function `f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt(1-sin^2x)+tanx/sqrt(1-sec^2x-1)+cotx/sqrt(1-cosec^2x-1)` whenever it is defined is

Options

A. 4
B. -2
C. 0
D. 2

Answer

B

Explanation

`f(x) =sinx/sqrt(1-cos^2x)+(cosecx)/sqrt(1-sin^2x)`
`+.tanx/sqrt(sec^2x-1)+cotx/sqrt(cosec^2x-1)`
`=sinx/abssinx+cosx/abscosx+tanx/abstanx+cotx/abscotx`
`={{:(4","" "x in"1st quadrant"),(-2","" "x in "2nd quadrant"),(0","" "x in " 3rd quadrant"),(-2"," " "x in "4th quadrant"):}`
`f(x)_("min")=-2`