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For 0<x1<x2<pi/2, prove that (x2)/(x1)<(...

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we have to prove that
`(x_(2))/(x_(1))lt(tanx_(2))/(tanx_(1)) or (tanx_(1))/(tanx_(1))lt(tanfx_(2))/(x_(2))`
Now consider ` f(x)=(tanx)/(x)`
Now consider f(x)=`(tanx)/(x)`
`therefore f(x) =(xsec^(2)x-tanx)/(x^(2))`
`=sec^(2)x(x-sin2x)/(2x^(2)cos^(2)x)`
Now `x in (0,pi//2)`
or `f(x_(1))ltf(x_(2))`
or `(tanx_(1))/(x_(1)) lt(tanx_(2))/(x_(2))`
or `(x_(2))/(x_(1))lt(tanx_(2))/(tan x_(1))`
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