Home
Class 12
MATHS
The number of all possible values of the...

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

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|22 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

The number of all possible values of theta, where 0

x sin ^ (3) theta + y cos ^ (3) theta = sin theta cos theta and x sin theta = y cos theta Find the value of x ^ (2) + y ^ (2)

If x sin^(3)theta+y cos^(3)theta=sin theta cos theta and x sin theta=y cos theta Find the value of x^(2)+y^(2)

If x sin^(3) theta + y cos^(3) theta = sin theta cos theta and x sin theta = y cos theta , then the value of x^(2) + y^(2) is :

If 0 lt theta lt pi and the system of equations (sin theta) x + y + z = 0 x + (cos theta) y + z = 0 (sin theta) x + (cos theta) y + z = 0 has a non-trivial solution, then theta =

If x sin^(3)theta+y cos^(3)theta=sin theta cos theta andx sin theta=y cos theta prove that x^(2)+y^(2)=1

If 3 sin 2 theta = 2 sin 3 theta and 0 lt theta lt pi , then sin theta =

Number of values of theta lying I [0,100 pi ] for which the system of equations (sin 3 theta ) x-y+z=0, (cos 2 theta ) x+4y +3z=0, 2x+ 7y+7z =0 has non-trivial solution is "____"

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

  2. Let -1/6 < theta < -pi/12 Suppose alpha1 and beta1, are the root...

    Text Solution

    |

  3. The value of sum(k=1)^(13) (1)/(sin(pi/4 + ((k-1)pi)/(6))sin(pi/4 + (k...

    Text Solution

    |

  4. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

    Text Solution

    |

  5. The number of all possible values of theta, where 0 lt theta lt pi, f...

    Text Solution

    |

  6. For 0 lt theta lt pi/2, the solution (s) of sum(m=1)^(6) cosec (the...

    Text Solution

    |

  7. If sin^ 4 x/2+cos^4 x/3 =1/5 then

    Text Solution

    |

  8. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)6(...

    Text Solution

    |

  9. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

  10. If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is

    Text Solution

    |

  11. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  12. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

    Text Solution

    |

  13. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

    Text Solution

    |

  14. If A = sin^2x + cos^4 x, then for all real x :

    Text Solution

    |

  15. Let cos (alpha+beta) = 4/5 and sin(alpha-beta)=5/13 where 0<= alpha,...

    Text Solution

    |

  16. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

  17. A triangular park is enclosed on two sides by a fence and on the third...

    Text Solution

    |

  18. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

    Text Solution

    |

  19. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

    Text Solution

    |