anonymous
  • anonymous
Prove that cos2 2x – cos2 6x = sin 4x sin 8x
Mathematics
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
Let us start from the start..
anonymous
  • anonymous
it is cos^2...ok
Mimi_x3
  • Mimi_x3
\[cos^{2}2x -cos^{2}6x = sin4xsin8x\]?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes
Mimi_x3
  • Mimi_x3
have you tried cos^{2}2x = (1+cos4x)/2?
anonymous
  • anonymous
no
apoorvk
  • apoorvk
\[\cos^2 A - \cos^2 B = \sin(A+B)\sin(B-A)\] This is a standard formula. So, we need a proof right?
anonymous
  • anonymous
(1+cos4x)/2-(1+cos12x)/2 = (1+cos 4x+cos12x+cos4xcos12x)/2 and then defactorize the last term...and factorize the second and third term
anonymous
  • anonymous
@apoorvk yup proof needed..
anonymous
  • anonymous
@apoorvk it is cosA-cosBand not their squares for standard formula
anonymous
  • anonymous
\[\cos^2(2x) - \cos^2(6x) \implies (\cos(2x) - \cos(6x))(\cos(2x) + \cos(6x))\] So: Using: \[\cos(C) + \cos(D) = 2\cos(\frac{C+ D}{2})\cos(\frac{C-D)}{2})\] \[\cos(C) - \cos(D) = 2\sin(\frac{C+ D}{2})\sin(\frac{D-C}{2})\] \[(2\sin(4x) \sin(2x))(2\cos(4x)\cos(2x)) \implies (2\sin(2x)\cos(2x)) \cdot (2\sin(4x) \cos(4x))\] \[\implies \sin(4x) \cdot \sin(8x)\]
anonymous
  • anonymous
Using: \[2\sin(x)\cos(x) \implies \sin(2x)\]
anonymous
  • anonymous
I think above you by mistake written (B-A) @apoorvk
anonymous
  • anonymous
You are doing wrong I guess..
anonymous
  • anonymous
Rewrite for cos(A) - cos(B) = ??
anonymous
  • anonymous
@apoorvk u told me it is sin(a+b).sin(b-a) but u have written differ
apoorvk
  • apoorvk
yeah I have memory problems -.- Amnesia *sigh* *sniff*
anonymous
  • anonymous
\[\cos(A) - \cos(B) = 2\sin(\frac{A+B}{2}) \cdot \sin(\frac{B-A}{2})\]
anonymous
  • anonymous
And not sin(a-B) in the last..
anonymous
  • anonymous
@apoorvk if i use ur method we wont get that lol
apoorvk
  • apoorvk
NOOOOOOOO!!!!!!!!!!!!!!!!!! What have i been doing? /_\
apoorvk
  • apoorvk
Okay please tweak it and use it as needed, we know the procedure atleast. Or should I repost?
anonymous
  • anonymous
See: \[\cos^2(2x) - \cos^2(6x) = \sin(A+B)\sin(A-B) \implies \sin(2x - 6x)\sin(2x + 6x)\] Don't you think we get negative ??? @apoorvk
apoorvk
  • apoorvk
yeah i got it ate already - unfortunately i can't view my raw LateX codes (some stupid bug :\), so I'll have to edit it manually. NOOOOOO!!!!!!!!!
apoorvk
  • apoorvk
Sir what you think is correct, if you want a confirmation. -.-
anonymous
  • anonymous
There must be condition for doing this formula : I am discussing with you @apoorvk
anonymous
  • anonymous
The above said formula will work if B > A..
apoorvk
  • apoorvk
\[\cos^2A−\cos^2B\] \[=(\cos A+\cos B)(\cos A−\cos B)\] \[=[2\cos(\frac{A+B}2)\cos(\frac{A−B}2)][2\sin(\frac{A+B}2)\sin(\frac{B-A}2)]\] \[=[2\sin(\frac{A+B}2)\cos(\frac{A+B}2)][2\sin(\frac{B-A}2\cos(\frac{B-A}2)]\] \[=\Large\boxed{\sin(A+B)\sin(B-A)}\] Happy nitpickers? --____--
anonymous
  • anonymous
Do you think It will work ??
apoorvk
  • apoorvk
Water in eyes, Fish in Water \(\large \rightarrow\) so Fish in eyes. -_-
anonymous
  • anonymous
I am asking you @apoorvk
anonymous
  • anonymous
If fish is eyes then why are looking upwards?? Is fish in your eyes??
apoorvk
  • apoorvk
I paarsonaaally bilib it's Phaathar bill wa-ark! -,- (dish phormula)
anonymous
  • anonymous
What is this?? @apoorvk
apoorvk
  • apoorvk
U know aandarishtand? oowhaat u know no inglis?? BAH HUMBUG!
apoorvk
  • apoorvk
Inglish pipul go, liebe children behind -_-
apoorvk
  • apoorvk
'Addition', man, addition ----> " sin (A '+' B) - Y U LOVE SUBTRACTION??
anonymous
  • anonymous
Okay my mistake..
apoorvk
  • apoorvk
U inglish phail, I inglish oowhale. -____-
anonymous
  • anonymous
You failed in english? ok I got this.. Better luck next time.. @apoorvk
apoorvk
  • apoorvk
Hu shaid I phail in inglish?? U no si mai bandarfool inglish haan??? o.O I gets the 105 out of 100 -__- u get how many?

Looking for something else?

Not the answer you are looking for? Search for more explanations.