I have \(\displaystyle{\frac{{{e}^{{{y}{i}}}-{e}^{{-{y}{i}}}}}{{{e}^{{{y}{i}}}+{e}^{{-{y}{i}}}}}}\) , and I know

Kendall Daniels

Kendall Daniels

Answered question

2022-03-31

I have eyieyieyi+eyi , and I know that this equals
12(eyieyi)12(eyi+eyi)=sinh{yi}cosh{yi}=tanh{yi}
However, this is also supposed to equal itany. I'm not sure how to get to this result.
I tried doing
eyieyieyi+eyi=e2yi1eyie2yi+1eyi=e2yi1e2yi+1

Answer & Explanation

Cody Johns

Cody Johns

Beginner2022-04-01Added 8 answers

Consider
sinh(yi)=eyieyi2=ieyieyi2i=isin(y)
and
cosh(yi)=eyi+eyi2=cos(y)

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