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Question Number 752 by 112358 last updated on 06/Mar/15
Show that , ∀b∈R^+ , tan^(−1) b+tan^(−1) (1/b)=(π/2) .
Showthat,∀b∈R+,tan−1b+tan−11b=π2.
Answered by 123456 last updated on 06/Mar/15
lets f(x):=arctan x+arctan (1/x),x>0 f′(x)=(1/(1+x^2 ))−((1/x^2 )/(1+1/x^2 ))=(1/(1+x^2 ))−(1/(1+x^2 ))=0,x>0 f(x)=c,x>0 f(1)=arctan 1+arctan 1=(π/2)=c f(x)=(π/2),x>0
letsf(x):=arctanx+arctan1x,x>0f′(x)=11+x2−1/x21+1/x2=11+x2−11+x2=0,x>0f(x)=c,x>0f(1)=arctan1+arctan1=π2=cf(x)=π2,x>0

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