Answer:
B
Step-by-step explanation:
We want to determine an equivalent trignometric identity with the given expression:
[tex]\cos (x) - \cos^3 (x)[/tex]
We can factor out a cos(x):
[tex]=\cos (x) (1-\cos^2 (x))[/tex]
Recall from the Pythagorean Identity that:
[tex]\sin^2(x) + \cos^2(x) = 1[/tex]
Therefore:
[tex]\displaystyle \sin^2(x) = 1 - \cos^2(x)[/tex]
Substitute:
[tex]=\cos(x)(\sin^2(x))=\cos(x)\sin^2(x)[/tex]
Our answer is B.
