The hyperbolic cosine and the hyperbolic sine functions are def... | Filo
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SOLVED:The hyperbolic sine and hyperbolic cosine functions from ℝ to ℝ are defined by sinhx:=(e^x-e^-x)/(2) and coshx:=(e^x e^-x)/(2) for x ∈ℝ . Show that for any t ∈ℝ, the point (cosht, sinht) is on the hyperbola x^2-y^2=1. Also, show that (i) sinh0=0, cosh0=1 and cosh^2-sinh^2=1 for all x ∈ℝ. (ii) (sinh)^' x=coshx and (cosh)^' x=sinhx for all x ∈ℝ. (iii) sinh(x y)=sinhx coshy coshx sinhy and cosh(x y)=coshx coshy sinhx sinhy for all x, y ∈ℝ Sketch the graphs of the functions sinh and
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