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

Problem

cos(x)−cos(x)*sin^2(x)

Solution

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

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

cos(x)*(1−sin^2(x))

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

cos(x)*(cos^2(x))

4. Multiply the terms to simplify the expression to its final form.

cos^3(x)

Final Answer

cos(x)−cos(x)*sin^2(x)=cos^3(x)

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