$\text{sinh}\ x\ \text{cosh}\ y = \frac12(\text{sinh}(x + y) + \text{sinh} (x - y))$ Expression of hyperbolic functions in terms of others In the following we assume x > 0.

在 数学 中， 双曲函数 是一类与常见的 三角函数 （也叫圆函数）类似的函数。 最基本的双曲函数是 雙曲正弦 函数 和 雙曲餘弦 函数 ，从它们可以导出 双曲正切 函数 等，其推导也类似于三 …

\sinh (x+y) = \sinh x \cosh y + \cosh x \sinh y \\\cosh (x+y) = \cosh x \cosh y + \sinh \sinh y \\\tanh (x+y) = \frac {\tan x +\tanh y} {1 +\tanh x \tanh y} \\ 四、倍元公式. \sinh 2 x=2 \sinh x \cosh x …

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 …

双曲正弦函数是 双曲函数 的一种。 双曲正弦函数在 数学语言 上一般记作 sinh，也可简写成sh。 与 三角函数 一样，双曲函数也分为双曲正弦、双曲余弦、 双曲正切 、双曲余切、双曲正割、 …

公式3 \sinh^ {-1}x=\ln (x+\sqrt {x^2+1}),\cosh^ {-1}x=\ln (x+\sqrt {x^2-1}),\tanh^ {-1}x=\frac {1} {2}\ln\frac {1+x} {1-x}\\ \mathrm {csch}^ {-1}x=\ln\left (\frac {1+\sqrt {1+x^2}} {x}\right),\mathrm …

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What is the formula for sinh 3x? Flexi Says: The formula for @$\begin{align*}sinh ~3x\end{align*}@$ in terms of @$\begin{align*}sinh ~x\end{align*}@$ is given by:

2023年8月17日 · Using the definition of hyperbolic functions, we can show that sinh (3x) = 3sinh (x) + 4sinh^3 (x). We start by rewriting sinh (x) and cosh (x) in terms of exponential functions. …