Simplify (csc(x))/(cot(x))

Problem

csc(x)/cot(x)

Solution

1. Rewrite the numerator using the reciprocal identity csc(x)=1/sin(x)

2. Rewrite the denominator using the quotient identity cot(x)=cos(x)/sin(x)

3. Substitute these identities into the original expression to create a complex fraction.

1/sin(x)/cos(x)/sin(x)

4. Multiply the numerator by the reciprocal of the denominator.

1/sin(x)⋅sin(x)/cos(x)

5. Cancel the common factor of sin(x) from the numerator and the denominator.

1/cos(x)

6. Apply the reciprocal identity 1/cos(x)=sec(x) to find the simplest form.

Final Answer

csc(x)/cot(x)=sec(x)

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