Simplify cos(x)^3+sin(x)^2cos(x)

Problem

cos3(x)+sin2(x)*cos(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)*(cos2(x)+sin2(x))

3. Apply the Pythagorean identity which states that sin2(x)+cos2(x)=1

cos(x)*(1)

4. Simplify the resulting expression by performing the multiplication.

cos(x)

Final Answer

cos3(x)+sin2(x)*cos(x)=cos(x)

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