prove-that-tan-x-sinh-y-if-sin-x-tanh-y-

Question Number 81471 by jagoll last updated on 13/Feb/20

prove that

\tan (x) = \sinh (y) if \sin (x) =

\tanh (y) .

Commented by john santu last updated on 13/Feb/20

\Rightarrow \sin (x) = \tanh (y)

squaring \Rightarrow \sin^{2} (x) = \tanh^{2} (h)

1 - \sin^{2} (x) = 1 - \tanh^{2} (y)

\cos^{2} (x) = sech^{2} (y)

\cos (x) = sech (y)

we get \frac{\sin (x)}{\cos (x)} = \frac{\tanh (y)}{sech (y)} = \sinh (y)