Solveeit Logo
Login

Question

Question: If \(\sin(x + iy) = A + iB,\) then A equals....

If sin⁡(x+iy)=A+iB,\sin(x + iy) = A + iB, then A equals.

A

sinh⁡xcos⁡y\sinh x\cos y

B

sin⁡xcos⁡hy\sin x{\cos h}y

C

cos⁡xsinh⁡y\cos x\sinh y

D

cos⁡hxsin⁡y{\cos h}x\sin y

Answer

sin⁡xcos⁡hy\sin x{\cos h}y

Explanation

Solution

sin⁡(x+iy)=A+iB\sin(x + iy) = A + iB

sin⁡xcos⁡iy+cos⁡xsin⁡iy=A+iB\sin x\cos iy + \cos x\sin iy = A + iB

sin⁡xcos⁡hy+cos⁡xsin⁡hy=A+iB\sin x{\cos h}y + \cos x{\sin h}y = A + iB

sin⁡xcos⁡hy=A\sin x{\cos h}y = A