Simplify sin(x)*cot(-x)

Problem

sin(x)*cot(−x)

Solution

1. Apply the odd-even identity for the cotangent function, which states that cot(−x)=−cot(x)

sin(x)*cot(−x)=sin(x)*(−cot(x))

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

sin(x)*(−cot(x))=−sin(x)cos(x)/sin(x)

3. Simplify the expression by canceling the sin(x) terms in the numerator and denominator.

−sin(x)cos(x)/sin(x)=−cos(x)

Final Answer

sin(x)*cot(−x)=−cos(x)

Want more problems? Check here!