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If the maximum and minimum values of sin...

If the maximum and minimum values of `sinx/(sqrt(1-cos^2))+cosx/(sqrt(1-sin^2x))+tanx/(sqrt(sec^2x-1))+cotx/(sqrt(cosec^2-1))` when it is defined are M and m respectively then the values of M-m is

A

4

B

-2

C

0

D

2

Text Solution

Verified by Experts

`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`
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