Q. $\frac{1 + {tanh\ }\frac{x}{2}}{1 - {tanh\ }\frac{x}{2}}$ is equal to
A) $e^{- x}$
B) $e^{x}$
C) $2e^{x/2}$
D) $2e^{- x/2}$
Explanation
(b)
$\frac{1 + {tanh\ }\frac{x}{2}}{1 - {tanh\ }\frac{x}{2}} = \frac{\cosh\frac{x}{2} + {sinh\ }\frac{x}{2}}{\cosh{\frac{x}{2} -}{sinh\ }\frac{x}{2}} = \frac{e^{x/2\ }}{e^{- x/2\ }} = e^{x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.