1.

If 0 alpha ltbeta lt pi/2 then

Answer»

`(tan beta)/(tan alpha ) LT (alpha)/(beta)`
`(tan beta)/(tan alpha) gt (alpha)/(beta)`
`(tan beta )/(tan alpha )gt (alpha)/(beta)`
`(tan alpha)/(tan beta )le (alpha)/(beta)`

Solution :CONSIDER the FUNCTION f(X) given `by f(x)=x tan x, x in(0 , pi //2)`
we have ,
`f(x) = x sec^2 x + tan x gt 0 " for all " x In (0,pi//2)`
`rArrf(x) is increasingon (0,pi//2)`
`rArrf(alpha)lt f (beta) for 0 alpha lt beta lt (pi)/(2)`
`rArralpha tan alpha lt beta `
`rArr /beta(tan beta)/(tan alpha)`


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