Home
Class 12
MATHS
Let A and B denote the statements A : ...

Let `A and B` denote the statements
`A : cos alpha + cos beta + cos gamma =0`
`B : sin alpha + siin beta + sin gamma = 0`
If `cos(beta - gamma) + cos (gamma -alpha) + cos (alpha -beta) = - (3)/(2)`,
then

A

A is true and B is false

B

A is false and B is true

C

Both A and B are true

D

Both A and B are false

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|34 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)|30 Videos

Similar Questions

Explore conceptually related problems

Let A and B denote the statements A: "cos"alpha+"cos"beta+"cos"gamma=""0 B : "sin"alpha+"sin"beta+"sin"gamma=""0 If cos(beta-gamma)""+""cos(gamma-alpha)""+""cos(alpha-beta)""=""""-(3//2) , then (1) A is true and B is false (2) A is false and B is true (3) both A and B are true (4) both A and B are false

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If cos alpha + 2 cos beta +3 cos gamma = sin alpha + 2 sin beta + 3 sin gamma y = 0 , then the value of sin 3alpha + 8 sin 3beta + 27 sin 3gamma is

cos alphasin(beta-gamma)+cosbetasin(gamma-alpha)+cos gammasin(alpha-beta)=

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gamma and b/c+c/a+a/b=1, then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=

If cos^(-1) alpha + cos^(-1) beta + cos^(-1) gamma = 3pi , then alpha (beta + gamma) + beta(gamma + alpha) + gamma(alpha + beta) equal to

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

VMC MODULES ENGLISH-TRIGONOMETRIC IDENTITIES AND EQUATIONS -JEE Main (Archive)
  1. Let alphaa n dbeta be nonzero real numbers such that 2(cosbeta-cosalph...

    Text Solution

    |

  2. Let f: (-1, 1) to R be such that f(cos 4theta) = (2)/(2-sec^(2)theta) ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let varphi,phi in [0,2pi] be such that 2costheta(1-sinphi)=sin^2theta(...

    Text Solution

    |

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

    Text Solution

    |

  6. The number of distinct solution of the equation 5/4 cos^(2) 2x + cos^(...

    Text Solution

    |

  7. The positive integer value of n >3 satisfying the equation 1/(sin(pi/n...

    Text Solution

    |

  8. The number of values of theta in the interval (-pi/2, pi/2) such that ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If (sin^(4)x)/(2)+(cos^(4)x)/(3)=1/5, then

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. The number of ordered pairs (alpha, beta) ,where alpha, beta in (-pi, ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The expression (tan A)/(1-cotA)+(cot A)/(1-tan A) can be written as

    Text Solution

    |

  17. In a Delta PQR , if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1, th...

    Text Solution

    |

  18. If A=sin^(2)x+cos^(4)x, then for all real x

    Text Solution

    |

  19. Let cos(alpha + beta) = 4//5 and let sin ( alpha - beta)= 5//13, wher...

    Text Solution

    |

  20. Let A and B denote the statements A : cos alpha + cos beta + cos gam...

    Text Solution

    |