$\text{cosh}^4 x = \frac{3}{8} + \frac12 \text{cosh}\ 2x + \frac18 \text{cosh}\ 4x$ Sum, difference and product $\text{sinh}\ x + \text{sinh}\ y = 2 \text{sinh}\ \frac12(x + y)\ \text{cosh}\ \frac12(x - y)$

\frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

Jul 25, 2023 · Answer: To prove the identity cosh 3x = 4 cosh^3 x - 3 cosh x, we'll use the definition of hyperbolic cosine (cosh) and the identity cosh^2 x - sinh^2 x = 1. Definition of hyperbolic cosine: cosh x = (e^x + e^(-x)) / 2

The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh(x) = e x − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh(x) = e x + e-x 2 (pronounced "cosh") They use the natural exponential function e x. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary

The formula for @$\begin{align*}cosh(3x)\end{align*}@$ is given by: @$\begin{align*}cosh(3x) = 4cosh^3(x) - 3cosh(x)\end{align*}@$

It is a tool that computes the values of six basic hyperbolic functions – sinh, cosh, tanh, coth, sech, and csch – all in a blink of an eye. You can also use it to calculate the inverse hyperbolic functions.

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What is the integral of $\cosh^3(x)$? And how exactly can I calculate it? I've tried setting $\cosh^3(x)=(\frac{e^x+e^{-x}}{2})^3$ but all I get in the end is one long fraction.

Feb 24, 2021 · $\cosh 3 x = 4 \cosh^3 x - 3 \cosh x$ where $\cosh$ denotes hyperbolic cosine. Proof