If $ \frac{x}{y} = cot \theta $, where $\theta $ is  an acute angle, then $ cosec \theta $ = _________.

Solution:

Given:
$ \frac{x}{y} = \cot \theta $

We know:
$ \cot \theta = \frac{\text{base}}{\text{perpendicular}} $

So,
Base = x, Perpendicular = y

Hypotenuse:
$ = \sqrt{x^2 + y^2} $

Now,
$ \csc \theta = \frac{\text{hypotenuse}}{\text{perpendicular}} $

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

Final Answer:

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