InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3)`, prove that `x y+y z+z x=0.` |
|
Answer» Let `xcostheta = ycos(theta+(2pi)/3) = zcos(theta+(4pi)/3) = k` Then, `k/x = cos theta, k/y =cos(theta+(2pi)/3), k/z = cos(theta+(4pi)/3)` `:.k(1/x+1/y+1/z) = cos theta +cos(theta+(2pi)/3) + cos(theta+(4pi)/3)` `=>k(1/x+1/y+1/z) = (cos theta +cos(theta+(4pi)/3)) + cos(theta+(2pi)/3)` `=>k(1/x+1/y+1/z) = (2cos(theta+(2pi)/3)cos((-2pi)/3)) + cos(theta+(2pi)/3)` `=>k(1/x+1/y+1/z) = (2cos(theta+(2pi)/3)cos((2pi)/3)) + cos(theta+(2pi)/3)` `=>k(1/x+1/y+1/z) = (2cos(theta+(2pi)/3)(-1/2)) + cos(theta+(2pi)/3)` `=>k(1/x+1/y+1/z) = -cos(theta+(2pi)/3) + cos(theta+(2pi)/3)` `=>1/x+1/y+1/z = 0` `=>(yz+zx+xy)/(xyz) = 0` `=>xy+yz+zx = 0` |
|