Home
Class 12
MATHS
If f(x)={:[(cosx,-sinx,0),(sinx,cosx,0),...

If `f(x)={:[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)]` show that `f(alpha)f(beta)=f(alpha+beta)`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NCERT BANGLISH|Exercise EXERCISE 3.3|14 Videos

  • MATRICES

    NCERT BANGLISH|Exercise EXERCISE 3.4|18 Videos

  • MATRICES

    NCERT BANGLISH|Exercise EXERCISE 3.1|10 Videos

  • LINEAR PROGRAMMING

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE|8 Videos

  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

Similar Questions

Explore conceptually related problems

if f(x) = |{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that lim_(xto0)(f(x))/x^2=1

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

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

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

The function f(x)=(sinx)/(sinx-cosx) is discontinuous at -

If f(x)=|(sinx, cosx, tanx),(x^(3),x^(2),x),(2x,1,1)| then the value of lim_(x to 0) (f(x))/(x^(2)) is -

If f(x)=(x-1)(x-2)(x-3)(x-4) , show that the equation f'(x)=0 has three roots alpha, beta and gamma where 1 lt alpha lt 2, 2 lt beta lt 3 and 3 lt gamma lt 4 .

If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}| , then lim_(xto0)(f(x))/(x^(2))=

Let f(x)= |{:(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0):}| ,"then find " 1/piint_0^(pi/2)[f(x)+f'(x)]dx.

NCERT BANGLISH-MATRICES-EXERCISE 3.2
  1. Compute the indicated products: [(1),(2),(3)][(2,3,4)]

    Text Solution

    |

  2. If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(...

    Text Solution

    |

  3. If A=[((2)/(3), 1,(5)/(3)),((1)/(3), (2)/(3), (4)/(3)),((7)/(3), 2, (2...

    Text Solution

    |

  4. Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sin[(sint...

    Text Solution

    |

  5. Find X and Y, if (i) X+Y=[(7,0),(2,5)] and X-Y=[(3,0),(0,3)] (ii) ...

    Text Solution

    |

  6. Find X, if Y=[(3,2),(1,4)] and 2X+Y=[(1,0),(-3,2)]

    Text Solution

    |

  7. Find the values of x and y, if 2{:[(1,3),(0,x)]+{:[(y,0),(1,2)]={:[(...

    Text Solution

    |

  8. Solve the equation for x, y, z and t, if 2[(x, y),(z,t)]+3[(1,-1),(0,2...

    Text Solution

    |

  9. If x[(2),(3)]+y[(-1),(1)]=[(10),(5)], find the value of x and y.

    Text Solution

    |

  10. Given 3[(x,y),(z,w)]=[(x,6),(-1,2w)]+[(4,x+y),(z+w,3)], find the value...

    Text Solution

    |

  11. If f(x)={:[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] show that f(alpha)f(b...

    Text Solution

    |

  12. Show that (i) [(5,-1),(6,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(5,-1),(6...

    Text Solution

    |

  13. Find A^(2)-5A+6I, if A=[(2,0,1),(2,1,3),(1,-1,0)]

    Text Solution

    |

  14. If A=[(1,0,2),(0,2,1),(2,0,3)], prove that A^(3)-6A^(2)+7A+2I=0

    Text Solution

    |

  15. If A={:[(3,-2),(4,-2)], find k such that A^(2)=kA-2I(2)

    Text Solution

    |

  16. If A=[(0,-"tan"(alpha)/(2)),("tan"(alpha)/(2),0)] and I is the identit...

    Text Solution

    |

  17. A trust fund has Rs. 30,000 that must be invested in two different typ...

    Text Solution

    |

  18. The bookshop of a particular school has 10 dozen chemistry books, 8 do...

    Text Solution

    |

  19. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

    Text Solution

    |

  20. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

    Text Solution

    |