Verify the Identity (cot(x))/(csc(x))=cos(x)

Problem

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

Solution

1. Express in terms of sine and cosine by using the quotient identity cot(x)=cos(x)/sin(x) and the reciprocal identity csc(x)=1/sin(x)

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

2. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

cos(x)/sin(x)⋅sin(x)/1

3. Cancel common factors in the numerator and denominator, specifically sin(x)

cos(x)

4. Compare the result to the right side of the original identity to confirm they are equal.

cos(x)=cos(x)

Final Answer

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

Want more problems? Check here!