Question

Use a reciprocal identity to simplify sin(x)cot(x).

a) cos(x)
b) 1
c) tan(x)
d) csc(x)

Answer 1

Simplifying sin(x)cot(x) involves recognizing that cot(x) is the reciprocal of tan(x), which leads to the simplification to cos(x) by canceling out the sin(x) terms.

Step-by-step explanation:

To simplify sin(x)cot(x) using a reciprocal identity, we need to understand that the cotangent (cot(x)) is the reciprocal of the tangent function. Tangent is defined as tan(x) = sin(x)/cos(x), so cotangent is cot(x) = cos(x)/sin(x). Substituting this into our original expression, sin(x)cot(x), we get sin(x) multiplied by cos(x)/sin(x), which simplifies further to cos(x) because the sine terms cancel each other out.