Use basic identities to simplify the expression. cos θ - cos θ sin2θ

Question

Use basic identities to simplify the expression.          cos θ - cos θ sin2θ

anonymous · Answer

Well to begin do you know the double angle identity for sin?

anonymous · Answer

sin^2x + cos^2x = 1

anonymous · Answer

Not quite that is one of the Pythagorean Identities. The double angle identity for sin is:

$$\sin2\theta=2\sin \theta \cos \theta$$

anonymous · Answer

does that help at all?

anonymous · Answer

a little, but I'm still confused. Wouldn't that give me cosx - sin^2x?

anonymous · Answer

wait is that 2 in front of the theta an exponent or a 2 being multiplied by theta?

anonymous · Answer

It's an exponent

anonymous · Answer

Does this question have choices at all?

anonymous · Answer

sec2θ

 sin θ

 tan2θ

 cos3θ

anonymous · Answer

well first if this does help at all look for something in common, what can you take out of the problem or factor out that simplifies the expression. Think of something like a-ab=a(1-b)

anonymous · Answer

ummmmm.... can you factor out cos?

anonymous · Answer

yes! and your left with
cosθ(1−sin2θ)

Now think of the Pythagorean identity that you mentioned before, what can 
$$1-\sin^2\theta$$\
turn into?

anonymous · Answer

cos^2 x! So the answer would be cos^3 x!

anonymous · Answer

yes! correct!

anonymous · Answer

or as your choice is
$$\cos^3\theta$$

anonymous · Answer

Thank you so much!!!

anonymous · Answer

Your welcome :)