PROVE THAT COS Z,SIN Z,cosh Z and sinh z are entire function

Expert Solution

Colby Messinger answered 4 months ago

1-Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 1 2 ex +...

1-Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 1 2 ex + e−x + 1 2 = 1 2 = 2-Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x) sinh(y) = 1 2 (ex − e−x) 1 2 + 1 2 (ex + e−x) 1 2 = 1 4 + ex − y − e−x + y − e−x − y + ex + y...

Let f(x) = cosh(x) and g(x) = sinh(x), a = 0 and b = 1. A)...

Let f(x) = cosh(x) and g(x) = sinh(x), a = 0 and b = 1. A) Find the volume of the solid with base on the xy plane, bounded by the region above, whose cross-sections perpendicular to the x axis are squares. B) Find the volume of the solid formed if the region above is rotated about the line y = 4. C) Find the volume of the solid formed if the region above is rotated about the line x...

Prove that 1+ cos theta + cos 2theta + .... cos ntheta = 1/2 + (sin(n+1/2)theta)/2sin(theta/2)

verify the identities a.) (cos 8x + cos 4x) / (sin 8x - sin 4x) =...

verify the identities a.) (cos 8x + cos 4x) / (sin 8x - sin 4x) = Cot(2x) b.) tan^2(x/2) = 1 - 2cot(x)csc(x) + 2Cot^2x

proof Sin(A)-Sin(B), cos(A)+cos(B) Geometrically, A and B are acute angles

Prove or disprove whether the function f: Z x Z -> Z x Z given by...

Prove or disprove whether the function f: Z x Z -> Z x Z given by f(x,y) = (2x+y, 3x-6y) is injective, surjective or both.

Express sin 6θ as a polynomial in sin θ and cos θ.

a. (5 Marks) 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) =...

a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?

For the given function determine the following: f (x) = (sin x + cos x) 2...

For the given function determine the following: f (x) = (sin x + cos x) 2 ; [−π,π] a) Find the intervals where f(x) is increasing, and decreasing b) Find the intervals where f(x) is concave up, and concave down c) Find the x-coordinate of all inflection points

Write a matlab code for given task Use your ‘sin’ or ‘cos’ function to generate a...

Write a matlab code for given task Use your ‘sin’ or ‘cos’ function to generate a sinusoid wave having two components as f1 = 3kHz and f2 = 5kHz and then sample it with fs = 10kHz. Calculate its fft with zero frequency component in the middle. Plot it on a properly scaled w-axis. Specify if there is aliasing or not? If there is aliasing specify which component is casing the aliasing

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