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shubhamsrg
 3 years 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..
shubhamsrg
 3 years 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..

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i 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)

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

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

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0maybe @UnkleRhaukus and @ganeshie8

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0i 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 ?

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I think you took it seriously @vishweshshrimali5

vishweshshrimali5
 3 years ago
Best ResponseYou've already chosen the best response.0what ? @waterineyes

anonymous
 3 years ago
Best 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 \[x = 2n \pi \pm y\]

vishweshshrimali5
 3 years ago
Best ResponseYou've already chosen the best response.0yes......... trigonometric equations

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Check subhamarsh solution he is right in calculating this..

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0guys u already got it...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\cos(xy)+\cos(xz)+\cos(yz) \le1+1+1=3\]equality occurs when\[cos(xy)=\cos(xz)=\cos(yz)=1\]

shubhamsrg
 3 years ago
Best 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 ( )

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0That will not matter I think: \[\cos(\theta) = \cos(\theta)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I understand the feelings.. Ha ha ha...

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0sorry didnt catch ya ..come again..

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[y=x2n\pi\]\[z=x2m\pi\] put them in the first one \[\cos x+\cos (x2n\pi)+\cos(x2m\pi)=3\cos 30\]\[\cos x+\cos x+\cos x=3\cos 30\]

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0aha..i see..thanks again..
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