Question

Use basic identities to simplify the expression.
cos θ - cos θ sin^2θ

Answer 1

First you could factor out cos(theta)

Answer 2

\[\Large \cos(\theta)(1-\sin^2(\theta))\]

Answer 3

Can you go from there?

Answer 4

How did you factor out cos (theta)? Did you divide by cos(theta)?

Answer 5

@danber8 your final answer would be \[\cos ^{3}\]

Answer 6

cos^3 theta

Answer 7

Iseah, I'm confused as to how you got that answer

Answer 8

You don't divide, you see that therer's cos(theta) being multipled by those two terms so you FACTOR it not divide, factoring doesn't change the value

Answer 9

@Isaiah.Feynman thats why you're discouraged to give answers it doesn't help in the learning process, anyways \[\Large \cos(\theta)(1-\sin^2(\theta))=\cos(\theta)-\cos(\theta)\sin^2(\theta)\] your original equation, all we did was factor out a cos(theta)

Answer 10

I understand that now

Answer 11

Ok and do you have you're list of trig identities?

Answer 12

u mean like cos (theta) =sin(pi/2 - theta)?

Answer 13

Yes precisly and one of them is \[\sin^2(\theta)+\cos^2(\theta)=1\]
which can be moved around to \[\cos^2(\theta)=1-\sin^2()\]

Answer 14

\[\cos^2(\theta)=1-\sin^2(\theta)*\]

Answer 15

so now you can replace cos^2(theta) in the parentheses

Answer 16

Would we divide both sides by cos (theta)?

Answer 17

\[\cos(\theta)(1-\sin^2(\theta))=\cos(\theta)(\cos^2(\theta))\]

Answer 18

We're not dividing by anything, we don't even this equal to something, its jsut and expression like 3x+5, its not being set to anything all they're asking is to simplify

Answer 19

How did you know cos(theta)(1-sin^2(theta))= cos(theta)(cos^2(theta))?

Answer 20

because one of our trig identities is \[\Large \sin^2(\theta)+\cos^2(\theta)=1\] which when we subtract \[\Huge \sin ^{2}\left( \theta \right)\] form both sides we get
\[\Large \cos^2(\theta)=1-\sin^2(\theta)\]

Answer 21

so now plug the left side in our problem

Answer 22

So cos(theta) x cos^2(theta)=cos^3(theta)?

Answer 23

costheta-costhetasin^2theta
costheta(1-sin^2theta)
costheta(cos^2theta)
cos^3theta

Answer 24

So far after factoring we were at cos(x)(1-sin^2(x))

now since we idntifies 1-sin^2(x) to be cos^2(x)

so \[\Large \cos(\theta)(1-\sin^2(\theta))=\cos(\theta)(\cos^2(\theta))=\cos^3(\theta)\]

Answer 25

I understand now, thanks

Answer 26

Np.