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x^{2}-x-6=0 -x+3\gt 2x+1 ; line\:(1,\:2),\:(3,\:1) f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120)

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 …

Use the definition of cosh: cosh(0) = (exp(0) + exp(-0))/2 = 2 / 2 = 1. Use the identity cosh 2 x − sinh 2 x = 1 along with the fact that sinh is an odd function, which implies sinh(0) = 0. Read the …

The value of the hyperbolic functions sinh and cosh in the point 0 of the x-axis is, thanks to the properties of the exponential function, the same as the "normal trigonometric functions": The …

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 …

What is the value of cosh (0) ?

$\sinh \frac{x}{2} = \pm \sqrt{\frac{\cosh x - 1}{2}}$ [+ if x > 0, - if x . 0] $\cosh \frac{x}{2} = \sqrt{\frac{\cosh x + 1}{2}}$ $\tanh \frac{x}{2} = \pm \sqrt{\frac{\cosh x - 1}{\cosh x + 1}}$ [+ if x …

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Sep 7, 2015 · From your expression, you can derive this like so: expand with "angle sum": $\sinh x cosh(iy)+ \cosh x \sinh(iy)=0 \implies \sinh x\cos y+ i \cosh x\sin y=0$ (note the transform …