Question

How do you convert `rcos(x/2) - rsin(x/2) = 0` to rectangular form?

Answer 1

`color(green)(x=0)`

Explanation:

I have assumed that the given equation could be better expressed as
`color(white)("XXX")r cos(theta/2)-r sin(theta/2)=0`
to avoid using `x` which is normally associated with the rectangular form.

`rArr` `color(white)("XXX")cancel(r) cos(theta/2)=cancel(r) sin(theta/2)`

`rArr` `color(white)("XXX")theta/2 = pi/4 (color(gray)(+-kpi, k in ZZ))`

`rArr` `color(white)("XXX")theta = pi/2 (color(gray)(+-k2pi, k in ZZ))`

Therefore we have a vertical line through the origin,
or, in terms of rectangular elements, `x=0`