Simplify sin(-x)csc(x)

Problem

sin(−x)*csc(x)

Solution

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

sin(−x)=−sin(x)

2. Apply the reciprocal identity for the cosecant function, which states that csc(x)=1/sin(x)

csc(x)=1/sin(x)

3. Substitute these identities back into the original expression.

−sin(x)⋅1/sin(x)

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

−1

Final Answer

sin(−x)*csc(x)=−1

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