Question

Prove that sinh 2x=2tanhx/1+tanh^2x​

Answer 1

Step-by-step explanation:

In the given question,

We have to prove that LHS = RHS,

$sinh2x=\frac{2tanhx}{1+tanh^{2}x}$

Therefore, on solving the Right Hand Side first we get,

$=\frac{\frac{2sinhx}{coshx} }{1+\frac{sinh^{2}x}{cosh^{2}x} }\\\\=\frac{{2sinhx}.{cosh^{2}x} }{{(cosh^{2}x+sinh^{2}x}).coshx}\\\\=\frac{2sinhx.coshx}{1} \\\\=sinh2x$

Therefore, we can see that the Left Hand Side is equal to the Right Hand side of the equation.

That is, what we find is that,

LHS = RHS

That is,

sinh2x = sinh2x

Hence, Proved.