Question

Is $\tanh^{-1}\left(\sin 2 \left(x +\dfrac {\pi}{4}\right) \right) = \dfrac {1}{\pi} \ln \left( \cot ^2 x \right) $?

score 79 · Answer 1 · 2019-02-06 20:46:32

79

Views

Is $\tanh^{-1}\left(\sin 2 \left(x +\dfrac {\pi}{4}\right) \right) = \dfrac {1}{\pi} \ln \left( \cot ^2 x \right) $?

Published on 06 Feb 2019 - 20:46

score 197 · Answer 2 · 2019-02-12 23:11:04

197

Views

Simplification using hyperbolic trig identities

Published on 12 Feb 2019 - 23:11

score 96 · Answer 3 · 2019-02-14 23:12:29

96

Views

Integral of $\frac{1}{\sqrt{(z-z')^2 + s^2}}$

Published on 14 Feb 2019 - 23:12

score 441 · Answer 4 · 2019-02-15 09:49:11

441

Views

Show the inequalities $|\sinh x| \leq 3|x|$ and $| \cosh x - 1 | \leq 3|x|$ for $|x| \lt \frac{1}{2}$

Published on 15 Feb 2019 - 9:49

score 92 · Answer 5 · 2019-02-18 10:14:29

92

Views

Show $ \coth(sx)(\coth(sx)-\frac{1}{s}\coth(x))$ is increasing

Published on 18 Feb 2019 - 10:14

score 43 · Answer 6 · 2019-02-20 06:22:55

43

Views

Explain why a hyperbola with center $(m,n)$ has the parametrized curve $r(t) = (m + a cosh, n + b sinh)$ "laying" on it

Published on 20 Feb 2019 - 6:22

score 90 · Answer 7 · 2019-02-21 12:11:31

90

Views

Primitive of $\frac{1-a\cosh(x)}{(\cosh(x)-a)^2}$

Published on 21 Feb 2019 - 12:11

score 263 · Answer 8 · 2019-02-22 10:28:06

263

Views

Evaluating $\int_{-\infty}^{\infty}\frac{1-a\cosh(\alpha x)}{(\cosh(\alpha x)-a)^2}\cos(\beta x)\,dx$

Published on 22 Feb 2019 - 10:28

score 604 · Answer 9 · 2026-03-22 12:46:21

604

Views

Proving the Partial Fraction Decomposition of the Hyperbolic Cotangent Function by using Poisson Summation

Published on 22 Mar 2026 - 12:46

score 1.1k · Answer 10 · 2019-02-26 09:08:11

1.1k

Views

$|\cosh z|^2 = \cosh^2x + \sin^2y$

Published on 26 Feb 2019 - 9:08

score 378 · Answer 11 · 2019-03-01 19:11:26

378

Views

Show that $\frac{1}{\cosh(x)} + \log\left(\frac{\cosh(x)}{1+\cosh(x)}\right) \ge 0$

Published on 01 Mar 2019 - 19:11

score 1k · Answer 12 · 2019-03-03 18:27:25

1k

Views

Find the general solution of the linear ordinary differential equation

Published on 03 Mar 2019 - 18:27

score 219 · Answer 13 · 2019-03-04 20:39:22

219

Views

Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$

Published on 04 Mar 2019 - 20:39

score 3.4k · Answer 14 · 2019-03-06 15:23:56

3.4k

Views

asymptotic expansion of $\ln(\cosh(x))$

Published on 06 Mar 2019 - 15:23

score 75 · Answer 15 · 2019-03-09 15:23:44

75

Views

How should I solve this limits of a series which goes to infinity

Published on 09 Mar 2019 - 15:23

List Question

Is $\tanh^{-1}\left(\sin 2 \left(x +\dfrac {\pi}{4}\right) \right) = \dfrac {1}{\pi} \ln \left( \cot ^2 x \right) $?

Simplification using hyperbolic trig identities

Integral of $\frac{1}{\sqrt{(z-z')^2 + s^2}}$

Show the inequalities $|\sinh x| \leq 3|x|$ and $| \cosh x - 1 | \leq 3|x|$ for $|x| \lt \frac{1}{2}$

Show $ \coth(sx)(\coth(sx)-\frac{1}{s}\coth(x))$ is increasing

Explain why a hyperbola with center $(m,n)$ has the parametrized curve $r(t) = (m + a cosh, n + b sinh)$ "laying" on it

Primitive of $\frac{1-a\cosh(x)}{(\cosh(x)-a)^2}$

Evaluating $\int_{-\infty}^{\infty}\frac{1-a\cosh(\alpha x)}{(\cosh(\alpha x)-a)^2}\cos(\beta x)\,dx$

Proving the Partial Fraction Decomposition of the Hyperbolic Cotangent Function by using Poisson Summation

$|\cosh z|^2 = \cosh^2x + \sin^2y$

Show that $\frac{1}{\cosh(x)} + \log\left(\frac{\cosh(x)}{1+\cosh(x)}\right) \ge 0$

Find the general solution of the linear ordinary differential equation

Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$

asymptotic expansion of $\ln(\cosh(x))$

How should I solve this limits of a series which goes to infinity

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