Question

. Use trigonometric expressions to build an equivalent trigonometric identity with the given expression: cos (x) − cos3 (x) = ?

A)cos (x) sin (x)
B)cos (x) sin2 (x)
C)sin2 (x)
D)sin (x) cos2 (x)

Answer 1

Answer:

B

Step-by-step explanation:

We want to determine an equivalent trignometric identity with the given expression:

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

We can factor out a cos(x):

$=\cos (x) (1-\cos^2 (x))$

Recall from the Pythagorean Identity that:

$\sin^2(x) + \cos^2(x) = 1$

Therefore:

$\displaystyle \sin^2(x) = 1 - \cos^2(x)$

Substitute:

$=\cos(x)(\sin^2(x))=\cos(x)\sin^2(x)$

Our answer is B.