What is the reciprocal identity of sine, sin(x)?

The reciprocal identity for sine states that the sine function has a reciprocal relationship with the cosecant function. Specifically, the cosecant of an angle, denoted as csc(x), is defined as the reciprocal of the sine of that angle. Thus, we can express this identity mathematically as csc(x) = 1/sin(x).

Therefore, if you rearrange the equation, it becomes clear that sin(x) = 1/csc(x). This directly confirms that the reciprocal identity of sine is indeed represented by 1/csc(x), making it the correct answer in this context.

Other options relate to different trigonometric functions or their reciprocals, but they do not correctly represent the reciprocal of sine. Understanding how these functions relate to each other is crucial for mastering trigonometric identities and their applications in various mathematical problems.