If x = cos@ + isin@ , y = cos€ + isin€ ' prove

Question

that (x - y)/(x + y) = itan((@ - €))/2

step sir plz

Answer 1

Lat's just use u and v for ease of typing

x = cosu + i sinu
y = cosv + i sinv

(x-y)/(x+y) =

(cosu-cosv) + (sinu-sinv)i
-------------------------------
(cosu+cosy) + (sinu+siny)i

Now multiply top&bottom by the conjugate of the denominator, collect terms, and recall that

tan (u-v)/2 = sin(u-v)/(1+cos(u-v))

that will get you where you need to go.