If tanh(x) = 4/5 , find the values of the other hyperbolic functions at x.

Solution:

Given, tanh(x) = 4/5

We have to find the values of the other hyperbolic functions at x.

tanh²x - sech²x = 1

sech x = √1 + (4/5)² = √41/5

So, cosh x = 1/sech x = 5/√41

coth x = 1/tanh x = 1/4/5 = 5/4

sinh x = tanh x . cosh x = 4/5 . 5/√41 = 20/5√41 = 4/√41

cosech x = 1/sinh x = √41/4

Therefore, the values of other hyperbolic functions at x are sinh(x) = 4/√41, cosh(x) = 5/√41, cosech(x) = √41/4, sech(x) = √41/5 and coth(x) = 5/4.

If tanh(x) = 4/5 , find the values of the other hyperbolic functions at x.

Summary:

If tanh(x) = 4/5 , the values of the other hyperbolic functions at x are sinh(x) = 4/√41, cosh(x) = 5/√41, cosech(x) = √41/4, sech(x) = √41/5 and coth(x) = 5/4.