Home
Class 12
MATHS
If f (x)={:((cos x,-sin x,0),(sin x,cos...

If `f (x)={:((cos x,-sin x,0),(sin x,cos x,0),(0,0,1)):},"show that "(f(x))^(-1) = f(-x)`.

A

f(x)+f(y)

B

f(x)-f(y)

C

f(x).f(y)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise LEVEL 2|47 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . f(y) = f(x+y)

Given that F(x)=[{:(,cos x,-sin x,0),(,sin x,cos x,0),(,0,0,1):}]."If"in R Then for what values of y, F(x+y)=F(x)F(y)

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to

find the value for x F(x)=|[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]|

If f(x) is defined as follows: f(x)={{:(1,x,gt0),(-1,x,lt0),(0,x,=0):} Then show that lim_(xrarr0) f(x) does not exist.

If f(x)={{:(,(x-a)^(n)cos ((1)/(x-a)), x ne a),(,0,x=a):} then at x=a, f(x) is

If f(x)= {{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):} , then

f(x)=|{:(cos x, x, 1),(2sin x, x^(2), 2x),(tan x, x, 1):}|." Then find the vlue of lim_(x to 0) (f'(x))/(x).

f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if x =0):} at x = 0 .

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. If f (x)={:((cos x,-sin x,0),(sin x,cos x,0),(0,0,1)):},"show that "(...

    Text Solution

    |

  2. If A and B are square martrices of equal degree, then which one is co...

    Text Solution

    |

  3. If A=[(1,0,0),(0,1,1),(0,-2,4)],6A^-1=A^2+cA+dI, then (c,d)=

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. If A=[[alpha,0],[ 1, 1]] and B=[[1, 0],[ 5, 1]], find the values of al...

    Text Solution

    |

  6. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

    Text Solution

    |

  7. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

    Text Solution

    |

  8. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

    Text Solution

    |

  9. Let "f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x...

    Text Solution

    |

  10. The parameter on which the value of the determinant |[1,a...

    Text Solution

    |

  11. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

    Text Solution

    |

  12. Consider the set A of all matrices of order 3 xx 3 with entries 0 or 1...

    Text Solution

    |

  13. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

    Text Solution

    |

  14. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

    Text Solution

    |

  15. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  16. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

    Text Solution

    |

  17. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  18. Given , 2x-y+2z=2, x-2y+z=-4, x+y+lambdaz=4, then the value of lam...

    Text Solution

    |

  19. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  20. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

    Text Solution

    |

  21. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |