Home
Class 12
MATHS
Show that costheta.[{:(costheta,sintheta...

Show that `costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.`

Text Solution

Verified by Experts

The correct Answer is:
`[(1,0),(0,1)]`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NCERT GUJARATI|Exercise EXERCISE 3.3|14 Videos

  • MATRICES

    NCERT GUJARATI|Exercise EXERCISE 3.4|18 Videos

  • MATRICES

    NCERT GUJARATI|Exercise EXERCISE 3.1|10 Videos

  • LINEAR PROGRAMMING

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|6 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

Similar Questions

Explore conceptually related problems

Simplify : costheta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sintheta,-costheta),(costheta,sintheta):}]

If A=[{:(costheta,sintheta),(-sintheta,costheta):}] then prove that A^(n)=[{:(cosntheta,sinntheta),(-sinn theta,cosntheta):}],n inN .

Let f(theta)=sintheta(sintheta+sin3theta). then f(theta)

Prove the following identities: (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

Prove the following : (All angles are acute angles.) (sintheta+costheta)/(sintheta-costheta)+(sintheta-costheta)/(sintheta+costheta)=2/(sin^(2)theta-cos^(2)theta)

Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costheta+sintheta)+(cos^(3)theta-sin^(3)theta)/(costheta-sintheta)=2

If cos(2theta)=0" then "|{:(0,costheta,sintheta),(costheta,sintheta,0),(sintheta,0,costheta):}|^2="............"

If sectheta=13/5 , show that (2sintheta-3costheta)/(4sintheta-9costheta)=3

Let P={theta:sintheta-costheta=sqrt2cos theta} and Q={theta:sintheta+costheta=sqrt2sintheta} be two set. Then,

If tantheta=a/b , find the value of (costheta+sintheta)/(costheta-sintheta)

NCERT GUJARATI-MATRICES-EXERCISE 3.2
  1. Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (i...

    Text Solution

    |

  2. if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]a...

    Text Solution

    |

  3. A=[[2/3,1,5/3],[1/3,2/3,4/3],[7/3,2,2/3]] and B=[[2/5,3/5,1],[1/5,2/5,...

    Text Solution

    |

  4. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

    Text Solution

    |

  5. 2X+3Y=[[2,3],[4,0]] and 3X+2Y=[[2,-2],[-1,5]]

    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. Find x ,\ y ,\ z ,\ t if 2[x z y t]+3[1-1 0 2]=3[3 5 4 6] .

    Text Solution

    |

  9. ifx[{:(2),(3):}]+Y[{:(-1),(1):}]=[{:(10),(5):}],find the values of X ...

    Text Solution

    |

  10. Given 3[x y z w]-[x6-1 2w]+[4x+y z+w3] , find the values of x, y, z an...

    Text Solution

    |

  11. If F(x) =[(cos x, -sin x,0),(sin x,cos x,0),(0,0,1)] show that F(x)F(y...

    Text Solution

    |

  12. show that (i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,3),(3,4):}...

    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 A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

    Text Solution

    |

  16. Let A=[0-tan(alpha//2)tan(alpha//2)0] and I be the identity matrix ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |