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

Problem

(csc(x)*sin(x))/cot(x)

Solution

1. Identify the reciprocal identity for the cosecant function, which is csc(x)=1/sin(x)

2. Substitute this identity into the numerator of the expression.

(1/sin(x)⋅sin(x))/cot(x)

3. Simplify the numerator by canceling the sin(x) terms, noting that 1/sin(x)⋅sin(x)=1

1/cot(x)

4. Apply the reciprocal identity for the cotangent function, where 1/cot(x)=tan(x)

tan(x)

Final Answer

(csc(x)*sin(x))/cot(x)=tan(x)

Want more problems? Check here!