Write an identity that expresses the first function in terms of the second. Cot(x) in terms of csc(x)

Answer 1

To express cot(x) in terms of csc(x), we can use the reciprocal relationship between these trigonometric functions:

csc(x) = 1/sin(x) (Reciprocal identity)

cot(x) is the reciprocal of tan(x), and tan(x) can be expressed in terms of sin(x) and cos(x):

tan(x) = sin(x)/cos(x) (Definition of tan(x))

Using these two relationships, we can express cot(x) in terms of csc(x) as follows:

cot(x) = 1/tan(x)
= 1/(sin(x)/cos(x))
= cos(x)/sin(x)
= 1/(sin(x)/cos(x))
= cos(x)/sin(x)
= 1/(1/sin(x))
= sin(x) (Simplifying the expression)

Therefore, cot(x) in terms of csc(x) is equal to sin(x).