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

Problem

sin(x)*cos^2(x)−sin(x)

Solution

1. Identify the common factor in both terms of the expression.

2. Factor out the common term sin(x) from the expression.

sin(x)*(cos^2(x)−1)

3. Recall the Pythagorean identity sin^2(x)+cos^2(x)=1 which can be rearranged to cos^2(x)−1=−sin^2(x)

4. Substitute −sin^2(x) for the expression inside the parentheses.

sin(x)*(−sin^2(x))

5. Multiply the terms to reach the simplest form.

−sin^3(x)

Final Answer

sin(x)*cos^2(x)−sin(x)=−sin^3(x)

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