A community for students.
Here's the question you clicked on:
 0 viewing
shubhamsrg
 2 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
 2 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..

This Question is Closed

vikrantg4
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0i wont guess that'd be a good soln..thats just assumption..

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

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

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

shubhamsrg
 2 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 ?

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

vishweshshrimali5
 2 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

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

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

waterineyes
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0yes......... trigonometric equations

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

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

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

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

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

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

shubhamsrg
 2 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 ( )

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

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

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

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

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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0aha..i see..thanks again..
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.