Question

Can someone help me?? I don't understand.

Answer 1

\(\huge{\downarrow}\) That's what the question asks me.
Use an angle sum identity to verify the identity \[\cos2\theta = 2 \cos ^{2}\theta-1 \]

Answer 2

\[\cos( \theta + \theta)\] do you know the identity for this
like cos (a+b) this what they want you to do

Answer 3

@YanaSidlinskiy

Answer 4

Not really.

Answer 5

cos(a+b)=cosacosb-sinasinb
familiar with this one? this is sum of angles identity

Answer 6

Yes. I'm familiar with it:)

Answer 7

Do the same thing with cos(theta+theta)

Answer 8

What do you mean the same thing? do what you did above^?

Answer 9

instead of cos(a+b)
use cos(theta+theta) and play with it and see where you will go

Answer 10

Do you get my point?

Answer 11

a nd b are theta and theta lol

Answer 12

Yea. Lemme see.

Answer 13

okay, go ahead and try!

Answer 14

I'm doing it on paper first.

Answer 15

yea! do it^^ better for learning this

Answer 16

Lol, Ok. I *think* I got it.:
\[\cos (\theta+\theta)=\cos(\theta)\cos (\theta)-\sin(\theta)\sin()\]
Like that?

Answer 17

yes good! what else can you do

Answer 18

Forgot the: *theta*

Answer 19

don't worry haha

Answer 20

what else can you see in that now

Answer 21

Umm..I don't know..Like. What do you mean?

Answer 22

like what is cos(theta) times it self?

Answer 23

same for sin(theta)

Answer 24

Would it be 0? Cuz I really don't know.

Answer 25

No, like what is axa?

Answer 26

I really don't know. I'm not sure.

Answer 27

well axa=a^2 no?

Answer 28

a number times itself is that number squared!

Answer 29

Ok..But that's not the same thing with the other trigonometric above. That's different.

Answer 30

well the concept is the same! cos(theta)cos(thata)=cos^2(theta)

Answer 31

Oh..Wow.! Ok. *Duh*. Took me a little whileXD

Answer 32

the concept is if we have quantity times it self it will give us that quantity squared

Answer 33

is the same* i meant

Answer 34

so..What would I do now?

Answer 35

i do want you to be careful since cos if a function and a is some real number so they are different, but what i want you to know here is the concept. not that im saying a and cos are same quantity! get that!

Answer 36

Now we have cos^2(theta)-sin^2(theta) right?
agree?

Answer 37

Yes. I agree. Definitely!

Answer 38

I'll simplify to where infinity is at the moment: What is the next step from here basically...

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

Answer 39

Continue ^_^

Answer 40

okay, there is an identity that you need to apply here
can tell me which one?

Answer 41

we have done that adam! thanks though ^^
i want to go slow with her lol

Answer 42

The...Angle Sum? Or..That'd be different. Maybe the cos idenity? I dunno:( I'm just starting to learn thihs. So..I maybe answering some crazy stuff.

Answer 43

Give her a hint* I like "pythagoream" trig identities ;)

Answer 44

a^2+b^2=c^2??

Answer 45

yeah that identity but trig one.
in terms of cos and sin do you know it?

Answer 46

No.

Answer 47

okay. there is this identity that is called Pythagorean trig identity
cos^(theta)+sin^2(theta)=1. if you want the proof we can do it haha
it derived from right Pythagorean theorem that you already now
just using right angle trigonometry in unit circle

Answer 48

i forgot squared for cos haha

Answer 49

okay we can come back to the proof later, just i case
here is this helpful link that you can take a look at
http://andrewmath.com/m170/Trigonometry/DoubleHalfAngleIdent/DoubleAngles.pdf