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Question Number 178355 by Spillover last updated on 15/Oct/22
Show that   cosh x>sinh x
$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cosh}\:\mathrm{x}>\mathrm{sinh}\:\mathrm{x} \\ $$
Answered by Ar Brandon last updated on 16/Oct/22
coshx−sinhx=(1/2)((e^x +e^(−x) )−(e^x −e^(−x) ))=e^(−x) >0  ⇒coshx>sinhx
$$\mathrm{cosh}{x}−\mathrm{sinh}{x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\left({e}^{{x}} +{e}^{−{x}} \right)−\left({e}^{{x}} −{e}^{−{x}} \right)\right)={e}^{−{x}} >\mathrm{0} \\ $$$$\Rightarrow\mathrm{cosh}{x}>\mathrm{sinh}{x} \\ $$
Commented by Spillover last updated on 16/Oct/22
thanks
$${thanks} \\ $$

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