反双曲函数基本公式 \sinh^ {-1} x \pm \sinh^ {-x} y = \sinh^ {-1} \left ( \sinh^ {-1}x \sqrt {1+y^2} \pm y \sqrt {1 +x^2} \right) \\\cosh ^ {-1} x \pm \cosh ^ {-1} y = \cosh^ {-1} \left [ xy \pm \sqrt { (x^2 …

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 …

2016年5月4日 · How do you show (cosh x + sinh x)n = cosh(nx) + sinh(nx) for any real number n? Use the definition coshx = ex + e−x 2 and sinhx = ex −e−x 2. Left Side: [ex +e−x 2 + ex − e−x …

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch Definition of hyperbolic functions Hyperbolic sine of x \displaystyle \text {sinh}\ x = \frac {e^ {x} - e^ {-x}} {2} sinh x = 2ex −e−x …

2016年4月28日 · You can easily generalize this to show that if n, m n, m are positive integers and cosh(nx) cosh (n x) and cosh((n + m)x) cosh ((n + m) x) are rational, then cosh(mx) cosh (m x) …

Hyperbolic Functions The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh (x) = ex − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh (x) = ex + e-x 2 …

这里介绍一些有关 双曲三角函数 的恒等式，它们是 三角函数 的 三角恒等式 推广。 归一恒等式. {\displaystyle \cosh^2 x - \sinh^2 x = 1, \quad \tanh^2 x + \operatorname {sech}^2 x = 1, \quad …

2024年7月4日 · 该代码使用Sympy库计算了曲线y = cosh (x)在x轴和两条竖直线x = a和x = b之间的面积。 Sympy的integrate ()函数用于计算积分。 cosh函数在求解一阶微分方程中具有重要作 …

2020年12月7日 · Prove that (cosh (x) + sinh (x))^n = cosh (nx) + sinh (nx)If you enjoyed this video please consider liking, sharing, and subscribing.Udemy Courses Via My Website...

2017年10月16日 · Prove that (cosh x + sinh x)n = cosh nx + sinh nx? Please see below. As coshx = ex + e−x 2 and sinhx = ex −e−x 2. and adding two coshx +sinhx = ex. and (coshx + sinhx)n …