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

Problem

sin(x)−sin(x)*cos^2(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)*(1−cos^2(x))

3. Apply the Pythagorean identity which states that sin^2(x)+cos^2(x)=1 meaning 1−cos^2(x)=sin^2(x)

sin(x)*(sin^2(x))

4. Multiply the terms to reach the simplest form.

sin^3(x)

Final Answer

sin(x)−sin(x)*cos^2(x)=sin^3(x)

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