(cos Θ − cos Θ)2 + (cos Θ + cos Θ)2

Question

anonymous · Answer

@mathmale

mathmale · Answer

JSD:  First I'm going to ask you to please type in those exponents properly.  The square of x would properly be typed in as x^2.
Secondly, please double-check to ensure that you've copied this problem down properly.  I ask you to do this because  $$(\cos \theta-\cos \theta)=0.$$

anonymous · Answer

(cos Θ − cos Θ)^2 + (cos Θ + cos Θ)^2

anonymous · Answer

thats right

mathmale · Answer

what is the value of cos theta - cos theta?

mathmale · Answer

sorry I have to excuse myself, I'll be back

anonymous · Answer

would it be cos^2θ then?

anonymous · Answer

and alright

anonymous · Answer

and to answer your question ) correct

anonymous · Answer

0*

mathmale · Answer

Still on the phone but will help you as far and as soon as I can.
no, cos theta - cos theta would be zero, not (cos theta)^2.

anonymous · Answer

yah i know i said zero i thought that was the answer

anonymous · Answer

and nah take your time

mathmale · Answer

You have two squares.
If you've copied the problem down correctly, the first (the left one) is zero.  
The second is (cos theta + cos theta)^2.  Do you agree with that?

If so, evaluate it.  (Still on phone.)

mathmale · Answer

Hint:  add cos theta to cost theta.  Result?

anonymous · Answer

yah i agree thats whu i thought it was cos^2θ… and it would be cos^2 correct

anonymous · Answer

?

anonymous · Answer

oooh wait

mathmale · Answer

Important that you write this as (2 cos x)^2 or $$(2 \cos \theta )^2~or~2^2\cos ^{2}\theta $$

anonymous · Answer

alright so same thing

anonymous · Answer

so when you add ^2 it would be 4cos^2 Θ correct?

mathmale · Answer

Essentially, yes.  You're not "adding ^2"; instead, you are SQUARING 2 cos theta.

anonymous · Answer

thats what i ment sorry

mathmale · Answer

I'm picky because this language needs to be precise.

mathmale · Answer

So, what do you believe is the final answer?  Please follow one of the examples of formatting that I've given you.

anonymous · Answer

I understand and you are right ! thx for the help i understand it a lot better now and thx for walking me through it.

anonymous · Answer

4cos^2 theta

mathmale · Answer

i would still prefer that you write that as 4 (cos theta)^2 or $$4 \cos ^{2}theta$$ for maximum clarity.

mathmale · Answer

Any further questions about this problem?