Home
Class 12
MATHS
If A=[(cos^(2)alpha, cos alpha sin alpha...

If `A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)]` and `B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)]` are two matrices such that the product AB is null matrix, then `alpha-beta` is

A

`alpha=beta`

B

`cos (alpha-beta)=0`

C

`sin(alpha-beta)=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 2|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

{:A=[(cos^2 alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)]:} {:B=[(cos^2 beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)]:} are two matrices such that the product AB is the null matrix, then (alpha-beta) is

If A,=[[cos alpha,-sin alphasin alpha,cos alpha]] and B=,[[cos beta,cos alpha]] and B=[[cos beta,-sin betasin beta,cos betasin beta,cos beta]] then show that AB=BA

Prove that the product of the matrices [[cos^2alpha, cosalphasinalpha],[cosalphasinalpha,sin^2alpha]] and [[cos^2beta,cosbetasinbeta],[cosbetasinbeta,sin^beta]] is the null matrix when alpha and beta differ by an odd multiple of pi/ 2.

Evaluate ,,,|cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha,cos beta,sin alpha sin beta,cos alpha]|

det[[cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha cos beta,sin alpha sin beta,cos alpha]]

(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1

A = [[0, sin alpha, sin alpha sin beta-sin alpha, 0, cos alpha cos beta-sin alpha sin beta, -cos alpha cos beta, 0]]

sin ^ (2) alpha + sin ^ (2) (alpha-beta) -2sin alpha cos beta sin (alpha-beta) = sin ^ (2)

Evaluate: quad =|cos alpha cos beta cos alpha sin beta-sin alpha-sin beta cos beta0sin alpha cos beta sin alpha sin beta cos alpha|

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2...

    Text Solution

    |

  2. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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 t1=(tan theta)^(tan theta), t2=(tan theta)6(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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 sin(alpha-beta)=5/13 where 0<= alpha,...

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

    Text Solution

    |

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

    Text Solution

    |