Question

show that function cos2z is analytic function..​

Answer 1

Answer:

cos(z) = cos(x + iy) = cos(x) cos(iy) - sin(x) sin(iy) = cos(x) cosh(y) - i sin(x) sinh(y).

Expressing this as u(x,y) + iv(x, y), the Cauchy-Riemann conditions can be checked:

∂u/∂x = -sin(x)cosh(y) and ∂v/∂y = -sin(x) cosh(y) = ∂u/∂x for all (x, y)

∂u/∂y = cos(x) sinh(y) and ∂v/∂x = -cos(x) sinh(y) = - ∂u/∂y for all (x, y).

It follows that w = cos(z) is analytic everywhere in the plane.

Hope you got the answer.

Please mark me as branliest.