Prove that d/dz sin(z) = cos(z) using Cauchy-Riemann equations

Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

A:

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

A:

Q: Find div F and curl F if F(x, y, z) = 2eyi- 7 cos y j + 4 sin² z k. div F= curl F=

A:

Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

A:

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

A:

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: sin (z+27) =

A:

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: What is y = sin (xy)

A:

Q: Show that sec(z) – cos(z) + csc(z) – sin(z) – sin(z) tan(z) = cos(z) cot(z)

A:

Q: Parametric Diff. dy (x) Find dx X=2 Co₂ (2+) y= 6. Sin (+)

A:

Q: Differentiate (sin(ax+b)/cos(cx+d))

A:

Q: Find dr de = dr de (5+ sec 0) sin 0

A: