Simplify sin(-x)*cot(-x)

Problem

sin(−x)*cot(−x)

Solution

1. Apply even-odd identities to the trigonometric functions. The sine function is odd, so sin(−x)=−sin(x) The cotangent function is also odd, so cot(−x)=−cot(x)

sin(−x)=−sin(x)

cot(−x)=−cot(x)

2. Substitute these identities back into the original expression.

(−sin(x))*(−cot(x))

3. Multiply the negative signs. Since a negative times a negative is a positive, the expression simplifies to the product of the positive functions.

sin(x)*cot(x)

4. Use the quotient identity for cotangent, which states that cot(x)=cos(x)/sin(x)

sin(x)⋅cos(x)/sin(x)

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

cos(x)

Final Answer

sin(−x)*cot(−x)=cos(x)

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