Home
Class 12
MATHS
If xsina+ysin2a+zsin3a=sin4a xsinb+ysin...

If `xsina+ysin2a+zsin3a=sin4a` `xsinb+ysin2b+zsin3b=sin4b`, `xsinc+ysin2c+zsin3c=sin4c`, then the roots of the equation `t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi,` are (a)`sina ,sinb ,sinc` (b) `cosa ,cosb ,cosc` (c)`sin2a ,sin2b ,sin2c` (d) `cos2a ,cos2bcos2c`

A

`sin a, sin b, sin c`

B

`cos a, cos b, cos c`

C

`sin 2a, sin 2b, sin 2c`

D

`cos 2a, cos 2b, cos 2c`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Solved Examples : Single Option Correct Type Questions|2 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 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

In DeltaABC, if sin^2 A+ sin^2 B = sin^2 C , then the triangle is

Prove that a cos A + b cos B + c cos C = 4R sin A sin B sin C

In DeltaABC ,prove that: a) sin2A + sin2B-sin2C=4cosA cosB sinC

If A + B + C =pi , prove that : . sin A + sin B+sinC = 4 cos frac (A)(2) cos frac (B)(2) cos frac (C)(2) .

If A + B + C =pi , prove that : cos A - cos B + cos C= -1+4 cos frac (A)(2) sin frac (B)(2) cos frac (C)(2) .

If A+B+C=pi , prove that (cosA)/(sin B sinC)+(cos B)/(sin C sinA)+(cos C)/(sin A sinB)=2 .

If A + B + C =180^@ , prove that : sin^2 A+ sin^2 B+sin^2 C=2 (1+cos A cos B cos C) .

If A + B + C =pi , prove that : sin A + sin B -sin C = 4 sin frac (A)(2) sin frac (B)(2) cos frac (C)(2) .

If a, b,c be the sides of a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=90 are equal then sin^2 A/2, sin^2 B/2, sin^2 C/2 are in

If A+B+C=180^@, then prove that tan^2 (theta/2)=tan(B/2) tan(C/2). when cos theta(sin B+sin C)=sin A.

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If xsina+ysin2a+zsin3a=sin4a xsinb+ysin2b+zsin3b=sin4b, xsinc+ysin2c...

    Text Solution

    |

  2. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  3. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

    Text Solution

    |

  4. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  5. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

    Text Solution

    |

  6. The number of all possible values of theta, where 0 lt theta lt pi, fo...

    Text Solution

    |

  7. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

    Text Solution

    |

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

    Text Solution

    |

  9. Let theta in (0, pi/4) and t(1)=tan theta)^(tan theta), t(2)=(tan thet...

    Text Solution

    |

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

    Text Solution

    |

  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

    Text Solution

    |

  12. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |