Home
Class 12
MATHS
Show that the determinant Delta(x) given...

Show that the determinant `Delta(x)` given by `Delta(x)` =
`|{:(sin(x+alpha),cos(x+alpha),a+xsinalpha),(sin(x+beta),cos(x+beta),b+xsinbeta),(sin(x+gamma),cos(x+gamma),c+xsingamma):}|` is independent of `x`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Determinants Exercise 7:|3 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is

Find the area of the triangle whose vertices are : (a cos alpha, b sin alpha), (a cos beta, b sin beta), (a cos gamma, b sin gamma)

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

The value of the determinant Delta = |(cos (alpha + beta),- sin (alpha + beta),cos 2 beta),(sin alpha,cos alpha,sin beta),(- cos alpha,sin alpha,- cos beta)| , is

lim_(xto0) (sin(alpha+beta)x+sin(alpha-beta)x+sin2alphax)/(cos2betax-cos2alphax).x

if f(x)=(sin (x+alpha)/(sin(x+beta))),alpha ne beta then f(x) has

Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha) *sin(beta-delta) , then :

If ( cos x - cos alpha)/(cos x - cos beta) = ( sin^2 alpha cos beta)/(sin^2 beta cos alpha) then cos x =

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,a+b):}| = 4 abc

    Text Solution

    |

  2. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

    Text Solution

    |

  3. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

    Text Solution

    |

  4. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  5. Without expanding the determinant at any stage prove that |{:(-5,3+5i...

    Text Solution

    |

  6. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  7. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |

  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

    Text Solution

    |

  9. If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...

    Text Solution

    |

  10. Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...

    Text Solution

    |

  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

    Text Solution

    |

  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

    Text Solution

    |

  14. If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

    Text Solution

    |

  15. Show that in general there are three values of t for which the followi...

    Text Solution

    |

  16. Find dy/dx if y=13x-y^2

    Text Solution

    |

  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

    Text Solution

    |