Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Prove that cos2 2x – cos2 6x = sin 4x sin 8x

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question