Verify the Identity cot(-x)sin(x)=-cos(x)

Problem

cot(−x)*sin(x)=−cos(x)

Solution

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

cot(−x)=−cot(x)

2. Substitute the quotient identity for cotangent, expressing it in terms of sine and cosine.

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

3. Rewrite the left side of the equation using the previous steps.

−cos(x)/sin(x)⋅sin(x)

4. Simplify the expression by canceling the common factor of sin(x) in the numerator and denominator.

−cos(x)

Final Answer

cot(−x)*sin(x)=−cos(x)

Want more problems? Check here!