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If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,p...

If `y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi),` then find `(dy)/(dx)dot`

Text Solution

Verified by Experts

We have
`y=sqrt((1-cso2x)/(1+cos2x)),=sqrt((2sin^(2)x)/(2cos^(2)x))=sqrt(tan^(2)x)`
`=|tanx|," where "x in(0,(pi)/(2))cup((pi)/(2),pi)`
`={{:(tan x, x in(0,(pi)/(2)),),(-tan x, x in((pi)/(2),pi),):}`
`therefore" "(dy)/(dx)={{:(sec^(2)x",", x in(0,(pi)/(2)),),(-sec^(2) x",", x in((pi)/(2),pi),):}`
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