Question

i’m confused on this question. i’m taking a pretest and i haven’t fully learned this material, help!! thank you :) !

Answer 1

we have the expression

$cos(x)-cos^3(x)$

Remember that

$\begin{gathered} sin^2x+cos^2x=1 \\ cos^2x=1-sin^2x \end{gathered}$

substitute in the given expression

$\begin{gathered} cos(x)-cos^{3}(x) \\ cos(x)-cos^2(x)cos(x) \\ cos(x)-(1-sin^2x)cosx \\ cosx-cosx+cosxsin^2x \\ cosxsin^2x \end{gathered}$

therefore

The answer is the first option