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mitchelsewbaran
Group Title
Verify the identity.
cos 4u= cos^2(2u) sin^2 (2u)
 one year ago
 one year ago
mitchelsewbaran Group Title
Verify the identity. cos 4u= cos^2(2u) sin^2 (2u)
 one year ago
 one year ago

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mathslover Group TitleBest ResponseYou've already chosen the best response.2
Put 'u' as any angle ... let it be \(\large{\frac{\pi}{2}}\) .
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
What do you get now as : \(\large{\cos(4(\frac{\pi}{2}))}\) = ?
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Can you tell me @mitchelsewbaran
 one year ago

.Sam. Group TitleBest ResponseYou've already chosen the best response.1
I would use cos(4u) cos(2u+2u) Then by identity: cos(A+B)=cosAcosBsinAsinB cos(2u)cos(2u)sin(2u)sin(2u) cos^2(2u)sin^2(2u)
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Is that verification or proof @.Sam. I think we have to verify and not to prove
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
cos(4(π 2 )) = 1
 one year ago

.Sam. Group TitleBest ResponseYou've already chosen the best response.1
If they both equal then that's verifying too
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
right now solve this : \[\large{\cos^2(2(\frac{\pi}{2})) \sin^2(2(\frac{\pi}{2}))}\]
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
hold on
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
take your time
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
1?
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
yes can you tell me how you got that ?
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
I replaced that whole equation with cos(2pi). Taking the cosine of 2pi, I got 1
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
o.O a small mistake @mitchelsewbaran : see here: \[\large{\cos^2(2(\frac{\pi}{2}))  \sin^2(2(\frac{\pi}{2}))}\] \[\large{\cos^2(\pi)  \sin^2(\pi)}\] \[\large{10= 1}\]
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
oh srry about that
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
No problem I just corrected you and I hope that you will not repeat that again. Best of luck :)
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
I have only 2 more that I need to verify. I was wondering if you can help?
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.0
You cannot substitute a single value (or any finite number of values) to PROVE this. If you find one that doesn't work, that would be sufficient to DISprove it.
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Did you try yourself first?
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
can u help me verify these last 2?
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
there is not fight @mitchelsewbaran . sorry if you felt bad. @tkhunny the question is to verify .. and hence we have to put a value and verify it
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
@mathslover ok :)
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
no I didn't feel bad @mathslover
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.0
@mathslover Demonstrating one or two values is just not what it is asking. It must be verified for ALL values. Since you cannot enter infinitely many values, there must be other methods employed. Demonstrating \(x = \pi\) says nothing of \(x = \sqrt{2}\)
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Ok @mitchelsewbaran post the one question of that two there in "ask a question forum" and surely I will help you but the second one will be solved by you and I will check it... if you get any problem in any concept you can ask me.
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
ok :)
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
@mathlover u're awesome, bro :)
 one year ago

mitchelsewbaran Group TitleBest ResponseYou've already chosen the best response.1
;)
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
well I think @tkhunny has a point but still it is not given to verify for all values... it is just to verify.. but if we still go on for a proving method .. then it's surely not verifying
 one year ago

tkhunny Group TitleBest ResponseYou've already chosen the best response.0
No, this is just not the case. "Verify the Identity" has meant to provide a general proof for all possible values in the entire Domain  at least since 1972. I am familiar with no reference in any mathematical text that has ever meant anything else. If only a few values were to be sufficient, the problem statement would say something like this, "Verify a few values and formulate a conjecture on whether or not this statement is generally true." "Verify the Identity" means ALL of them  leaving nothing out.
 one year ago
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