The expression 1/sin x can be simplified as cosec x.

Steps to simplify 1/sin x:

To simplify 1/sin (x), we can use the reciprocal trigonometric function known as the cosecant function, denoted as cosec x. The cosecant of an angle x is defined as the reciprocal of the sine of that angle, which can be expressed as:

cosec x = ​1/sin x

Therefore, 1/sin (x) is equivalent to cosec x. This simplification is particularly useful in trigonometry, where expressing functions in terms of fundamental trigonometric ratios often leads to more concise and standardized representations. The cosecant function provides a straightforward way to represent the reciprocal of the sine function, facilitating mathematical expressions and calculations involving trigonometric identities.