You need to eliminate A from equation `xsinA - ycosA = sqrt(x^2 +y^2)` , hence, you need to raise to square both sides, such that:

`(xsinA - ycosA)^2 = (sqrt(x^2 +y^2))^2`

`x^2sin^2 A - 2xysinA*cosA + y^2cos^2A = x^2 + y^2`

`x^2sin^2 A - x^2- 2xysinA*cosA + y^2cos^2A - y^2= 0`

`x^2(sin^2 A - 1) - 2xysinA*cosA + y^2(cos^2A - 1) = 0`

You need to use the fundamental formula of trigonometry `sin^2 A + cos^2A = 1 ` such that:

`-x^2cos^2A- 2xysinA*cosA - y^2sin^2 A = 0 `

Factoring out -1 yields:

`x^2cos^2A +2xysinA*cosA + y^2sin^2 A = 0`

`(x cos A + y sin A)^2 = 0 => x cos A =-y sin A => tan A = -x/y`

**Hence, evaluating the relation between the angle A and x and y yields `tan A = -x/y` .**

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