Simplify csc(x)sin(x)-sin(x)^2

Problem

csc(x)*sin(x)−sin2(x)

Solution

1. Identify the trigonometric identity for the cosecant function, which is the reciprocal of the sine function.

csc(x)=1/sin(x)

2. Substitute this identity into the first term of the expression.

1/sin(x)⋅sin(x)−sin2(x)

3. Simplify the product in the first term by canceling the sine terms.

1−sin2(x)

4. Apply the Pythagorean identity sin2(x)+cos2(x)=1 to rewrite the expression.

1−sin2(x)=cos2(x)

Final Answer

csc(x)*sin(x)−sin2(x)=cos2(x)

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