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shubhamsrg
Group Title
if
cos x + cos y + cos z = 3 sin60
and
sin x + sin y + sin z = 3 cos60
then how do i prove that
x=pi/6 + 2k(pi)
y=pi/6 + 2l(pi)
and z=pi/6 + 2m(pi)
where k,l,m are integers..
 2 years ago
 2 years ago
shubhamsrg Group Title
if cos x + cos y + cos z = 3 sin60 and sin x + sin y + sin z = 3 cos60 then how do i prove that x=pi/6 + 2k(pi) y=pi/6 + 2l(pi) and z=pi/6 + 2m(pi) where k,l,m are integers..
 2 years ago
 2 years ago

This Question is Closed

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
i dont have perfect solution.. still i logically say that cos x +cos y + cos z = cos 30 + cos 30 + cos 30 which means x=y=z=pi/6 since sin and cos repeat after intervals of 2pi x = y = z = pi/6 + 2n(pi)
 2 years ago

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
@shubhamsrg
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
i wont guess that'd be a good soln..thats just assumption..
 2 years ago

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
lol yeah .. :P
 2 years ago

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
@waterineyes
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Thinking.. Ha ha ha.
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
@mukushla
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
offline.
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
i know,,just tagged him!! :P
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
maybe @UnkleRhaukus and @ganeshie8
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
i sq both and added them,,got cosx cosy + sinx siny + cosx cosz + sinx sinz + cosz cosy + sinz siny = 3 so its cos( ) + cos ( ) + cos ( ) = 3 where space inside ( ) denotes something now each cos ( ) = 1 but how do i reach my ans ?
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
@Callisto
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
\[\cos(xy) + \cos(yz) + \cos(z  x) = 3\]
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
well I recall something from \(2k\pi\) and that is demoirve's theorem from complex numbers which has a lot to do with such questions
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
I think you took it seriously @vishweshshrimali5
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
what ? @waterineyes
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
\(2k \pi\) is just coming from that fact that general solution of \(cos(x) = cos(y)\) is given by \[x = 2n \pi \pm y\]
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
yes......... trigonometric equations
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
we can write sin x = cos(90x)........ will that help ?
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Let me remind the formula for : \((a + b + c)^2\)
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
Yes.............. \(\large a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
 2 years ago

vishweshshrimali5 Group TitleBest ResponseYou've already chosen the best response.0
Now ?
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Check subhamarsh solution he is right in calculating this..
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Nothing..
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.3
guys u already got it...
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.3
\[\cos(xy)+\cos(xz)+\cos(yz) \le1+1+1=3\]equality occurs when\[cos(xy)=\cos(xz)=\cos(yz)=1\]
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
@mukushla how do we reach the ans from here?? also we dont know if it'll be xy or yx under ( ),,same argument for other ( )
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
That will not matter I think: \[\cos(\theta) = \cos(\theta)\]
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Oh wow....
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
I understand the feelings.. Ha ha ha...
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
sorry didnt catch ya ..come again..
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
xy = 2npi ,, xz = 2mpi,, after that..
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.3
\[y=x2n\pi\]\[z=x2m\pi\] put them in the first one \[\cos x+\cos (x2n\pi)+\cos(x2m\pi)=3\cos 30\]\[\cos x+\cos x+\cos x=3\cos 30\]
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
aha..i see..thanks again..
 2 years ago
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