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

Problem

cot(x)/csc(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the fundamental identities cot(x)=cos(x)/sin(x) and csc(x)=1/sin(x)

cot(x)/csc(x)=cos(x)/sin(x)/1/sin(x)

2. Multiply the numerator by the reciprocal of the denominator to simplify the complex fraction.

cos(x)/sin(x)⋅sin(x)/1

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

cos(x)

Final Answer

cot(x)/csc(x)=cos(x)

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