We need to simplify 1/sin x. Before simplifying first let us know what sine is.
The sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right angled triangle.
sin x = opposite/hypotenuse
1/sin x = 1 / opposite/hypotenuse
= hypotenuse / opposite
We know that cosec x = hypotenuse / opposite
Hence 1/sin x = cosec x
1/sinx = cosec x