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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..
 one year ago
 one year ago
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..
 one year ago
 one year ago

This Question is Closed

vikrantg4Best 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)
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i wont guess that'd be a good soln..thats just assumption..
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
Thinking.. Ha ha ha.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i know,,just tagged him!! :P
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
maybe @UnkleRhaukus and @ganeshie8
 one year ago

shubhamsrgBest 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 ?
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
\[\cos(xy) + \cos(yz) + \cos(z  x) = 3\]
 one year ago

vishweshshrimali5Best 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
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
I think you took it seriously @vishweshshrimali5
 one year ago

vishweshshrimali5Best ResponseYou've already chosen the best response.0
what ? @waterineyes
 one year ago

waterineyesBest 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 \[x = 2n \pi \pm y\]
 one year ago

vishweshshrimali5Best ResponseYou've already chosen the best response.0
yes......... trigonometric equations
 one year ago

vishweshshrimali5Best ResponseYou've already chosen the best response.0
we can write sin x = cos(90x)........ will that help ?
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
Let me remind the formula for : \((a + b + c)^2\)
 one year ago

vishweshshrimali5Best ResponseYou've already chosen the best response.0
Yes.............. \(\large a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
Check subhamarsh solution he is right in calculating this..
 one year ago

mukushlaBest ResponseYou've already chosen the best response.3
guys u already got it...
 one year ago

mukushlaBest ResponseYou've already chosen the best response.3
\[\cos(xy)+\cos(xz)+\cos(yz) \le1+1+1=3\]equality occurs when\[cos(xy)=\cos(xz)=\cos(yz)=1\]
 one year ago

shubhamsrgBest 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 ( )
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
That will not matter I think: \[\cos(\theta) = \cos(\theta)\]
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
I understand the feelings.. Ha ha ha...
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
sorry didnt catch ya ..come again..
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
xy = 2npi ,, xz = 2mpi,, after that..
 one year ago

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

shubhamsrgBest ResponseYou've already chosen the best response.0
aha..i see..thanks again..
 one year ago
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