InterviewSolution
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InterviewSolution
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The number of all possible values of `theta`, where `0 lt theta lt pi`, for which the system of equations `(y+z)cos 3 theta =(xyz) sin 3 theta ,x sin 3 theta =(2cos3theta)/y+(2sin3theta)/z and (x y z)sin3theta=(y+2z)cos3theta+ysin3theta` have a solution `(x_0,y_0,z_0)` wiith `y_0 z_0 !=0` is |
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Answer» Correct Answer - 3 We have `(y+z) cos 3 theta=(xyz) sin 3 theta` ...(1) `xyz sin 3 theta=(2 cos 3 theta)z+(2 sin 3 theta)y` ...(ii) `(xyz) sin 3 theta=(y+2z) cos 3 theta+y sin 3 theta` ...(iii) `:. (y+z) cos 3 theta=(2 cos 3 theta)z+(2 sin 3 theta)y` `=(y+2z) cos 3 theta+y sin 3 theta` `rArr y(cos 3 theta-2 sin 3 theta)=z cos 3 theta` and `y(sin 3 theta- cos 3 theta)=0` Since, `y, z ne 0, sin 3 theta-cos 3 theta=0` or `tan 3 theta=0` `rArr 3 theta=npi +pi/4, n in Z` `rArr theta=((4n+1)pi)/12, n in Z` `rArr theta=pi/12, (5pi)/12, (9pi)/12` |
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