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Q.

If f(x)=sin1xβαβ and g(x)=Tan1xβαx then show that   f1(x)=g1(x)(β<x<α)

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answer is 1.

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Detailed Solution

Let f(x)=sin1xβαβ

f1(x)=11xβαβddxxβαβddxsin1x=11x2

=1αxαβ1αβd(xβ)dx

=1αxαβ1αβ12xβ
f(x)=12(αx)(xβ).....(1)

And  g(x)=Tan1xβαx ddxtan1x=11+x2

g1(x)=11+xβαxddxxβαx

=αxαβ12xβαx(αx)(1)(xβ)(1)(αx)2

=αx(αx)2(αβ)xβαβ(αx)2=12(αx)(xβ).....(2)

from (1) & (2)  f1(x)=g1(x)

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