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

B

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.