write tanhx in terms of e, hence prove that tanh2x = ((2tanhx)/(1+tanh^2 x))


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 79735 by Rio Michael last updated on 27/Jan/20

$w r i t e t a n h x i n t e r m s o f e, h e n c e p r o v e t h a t$ $t a n h 2 x = \frac{2 t a n h x}{1 + {t a n h}^{2} x}$
	Answered by Henri Boucatchou last updated on 28/Jan/20
	$tanhx=((e^x −e^(−x) )/(e^x +e^(−x) )) tanh2x=((sh2x)/(ch2x))=((2shx chx)/(ch^2 x+sh^2 x)) we have { ((sh2x=2shx chx)),((ch2x=ch^2 x+sh^2 x)) :} ⇒ th2x=((sh2x)/(ch2x))=((2shx chx)/(ch^2 x+sh^2 x)) ⇒ tanh2x=((2((shx)/(chx)))/(1+(((shx)/(chx)))^2 ))=((2tanhx)/(1+tanh^2 x))$
	$t a n h x = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$ $t a n h 2 x = \frac{s h 2 x}{c h 2 x} = \frac{2 s h x c h x}{{c h}^{2} x + {s h}^{2} x}$ $w e h a v e {\begin{cases} s h 2 x = 2 s h x c h x \\ c h 2 x = {c h}^{2} x + {s h}^{2} x \end{cases} \Rightarrow t h 2 x = \frac{s h 2 x}{c h 2 x} = \frac{2 s h x c h x}{{c h}^{2} x + {s h}^{2} x}$ $\Rightarrow t a n h 2 x = \frac{2 \frac{s h x}{c h x}}{1 + {(\frac{s h x}{c h x})}^{2}} = \frac{2 t a n h x}{1 + {t a n h}^{2} x}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum