Home
Class 12
MATHS
if f(alpha,beta)=|[cos alpha,-sin alpha,...

if `f(alpha,beta)`=`|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[cos(alpha+beta),-sin(alpha+beta),1]|` then
(a) `f(300 , 200)=f(400 , 200)`
(b) `f(200 , 400)=f(200 , 600)`
(c) `f(100 , 200)=f(200 , 200)`
(d)none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

If sin alpha = sin beta and cos alpha = cos beta then-

The expression cos^2(alpha+beta)+cos^2(alpha-beta)-cos2alpha.cos2beta, is

|{:(cosalpha cos beta,cos alpha sin beta ,-sin alpha),(-sin beta,cos beta," "0),(sin alpha cosbeta ,sinalpha sin beta ,""cos alpha):}|

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

sin alpha + sin beta = a "and" cos alpha + cos beta = b (tan alpha + tan beta)/(1-tan alpha tan beta)=

"Evaluate "Delta ={:|( 0 , sin alpha ,-cos alpha ) ,( -sin alpha , 0 , sin beta ),( cos alpha , -sin beta , 0)|:}

If tanbeta =(sin alpha cos alpha)/(2 + cos^(2) alpha),"prove that " 3 tan (alpha -beta).=2 tan alpha

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!...

    Text Solution

    |

  2. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

    Text Solution

    |

  3. if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...

    Text Solution

    |

  4. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

    Text Solution

    |

  5. If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...

    Text Solution

    |

  6. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  7. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

    Text Solution

    |

  8. Let a ,b ,c be positive and not all equal. Show that the value of the ...

    Text Solution

    |

  9. if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)...

    Text Solution

    |

  10. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

    Text Solution

    |

  11. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

    Text Solution

    |

  12. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

    Text Solution

    |

  13. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

    Text Solution

    |

  14. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

    Text Solution

    |

  15. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

    Text Solution

    |

  16. Consider the system linear equations in x ,y ,a n dz given by (sin3the...

    Text Solution

    |

  17. If alpha,beta "and" gamma are real number without expanding at any sta...

    Text Solution

    |

  18. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

    Text Solution

    |

  19. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

    Text Solution

    |

  20. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

    Text Solution

    |