Prove that: \(\tanh(\log\sqrt3)=0.5\)

Q.1 (b) Prove that: \(\tanh(\log\sqrt3)=0.5\)

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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\(\tanh x=\frac{e^x-e^{-x}}{e^x+e^{-x}}\). With \(x=\log\sqrt3\): \(e^x=\sqrt3,\ e^{-x}=\frac{1}{\sqrt3}\).

\(\tanh(\log\sqrt3)=\frac{\sqrt3-\frac1{\sqrt3}}{\sqrt3+\frac1{\sqrt3}}=\frac{3-1}{3+1}=\frac24\)

\(\therefore\ \tanh(\log\sqrt3)=0.5\) (proved).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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