\(\sinh^{-1}(x) = \ln\left(x + \sqrt{x^2 + 1}\right)\)

AS/A-Level Maths Hyperbolic functions - Proving the Inverse Hyperbolic function of Sine

Geeth's Maths Tutorials

\(\cosh^{-1}(x) = \ln\left(x + \sqrt{x^2 - 1}\right)\)

AS/A-Level Maths Hyperbolic functions - Proving the Inverse Hyperbolic function of Sine

Geeth's Maths Tutorials

\(\tanh^{-1}(x) = \dfrac{1}{2}\ln\left(\dfrac{1 + x}{1 - x}\right),\ \lvert x \rvert \lt 1\)

AS/A-Level Maths Hyperbolic functions - Proving the Inverse Hyperbolic function of Tangent

Geeth's Maths Tutorials