Question

Verify that the equation is an identity. cotx/cscx=cosx To verify the identity, start with the more

Answer 1

The identity cot(x) / csc(x) = cos(x) is verified by expressing cot(x) as cos(x)/sin(x) and csc(x) as 1/sin(x), simplifying, and showing that the result is cos(x).

Step-by-step explanation:

The question is asking to verify the identity cot(x) / csc(x) = cos(x). To do this, let's start by understanding that cot(x) is the reciprocal of tan(x) and csc(x) is the reciprocal of sin(x). Therefore, cot(x) can be expressed as cos(x)/sin(x) and csc(x) as 1/sin(x).

Now, to verify the identity, we can substitute these expressions into the given equation:

(cos(x)/sin(x)) / (1/sin(x))
= cos(x)/sin(x) * sin(x)/1
= cos(x)

Since sin(x) in the numerator and denominator cancel out, we are left with cos(x), which was to be proved. Thus, we have successfully verified that the initial equation is indeed an identity.