$$\frac{sin\theta}{x} = \frac{cos\theta}{y}$$, then $$sin\theta-cos\theta$$ is equal to

$$\frac{sin\theta}{x} = \frac{cos\theta}{y}$$

Reaaranging the given data , we get

$${tan\theta}$$ = $$\frac{x}{y}$$

Now taking $${cos\theta}$$ common from $$sin\theta-cos\theta$$,we get

= $$cos\theta{(tan\theta) - 1}$$............(1)

Imagine a right angle triangle

From this triangle , we can calculate values of $$cos\theta$$ and $$tan\theta$$ and hence putting the values in equation 1

we get = $$\frac{y}{\surd (x^2 + y^2)}$$ ($$\frac{x}{y} $$- 1)

= $$\frac{x-y}{\sqrt{x^{2}+y^{2}}}$$