Verify the Identity sin(x)-sin(x)cos(x)^2=sin(x)^3

Problem

sin(x)−sin(x)*cos^2(x)=sin^3(x)

Solution

1. Factor out the common term sin(x) from the left side of the equation.

sin(x)*(1−cos^2(x))=sin^3(x)

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

sin(x)*(sin^2(x))=sin^3(x)

3. Simplify the expression by multiplying the terms.

sin^3(x)=sin^3(x)

Final Answer

sin(x)−sin(x)*cos^2(x)=sin^3(x)

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