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