Home
Class 12
MATHS
If A=((cosx,sinx),(-sinx,cosx)) then pro...

If `A=((cosx,sinx),(-sinx,cosx))` then prove that `A^n=((cosnx,sin nx),(-sin nx,cosnx)` for all positive integers n.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 3

    MODERN PUBLICATION|Exercise PROBLEM|63 Videos

  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 Videos

Similar Questions

Explore conceptually related problems

If y=tan^(-1)(cosx/(1+sinx)), then prove that dy/dx=-1/2

Write the value of int(cosx-sinx)/(sinx+cosx)dx .

If y=5cosx-3sinx ,then prove that (d^(2)y)/(dx^(2))+y=0

Prove that int_0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

Evaluate: int(3+2cosx+4sinx)/(2sinx+cosx+3) dx

If y =(cosx+sinx)/cosx, then what is dy/dx ?

If y=x^(sinx)+(sinx)^(cosx) , then find (dy)/(dx) .

If f(x)=[{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}] , then show that f(x)*f(y)=f(x+y) .

MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  2. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

    Text Solution

    |

  3. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

    Text Solution

    |

  4. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

    Text Solution

    |

  5. Find the dy/dx when x = a[cos t + log tan (t//2)], y = a sin t

    Text Solution

    |

  6. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

    Text Solution

    |

  7. inttan^-1(secx+tanx)dx

    Text Solution

    |

  8. If the magnitude of the difference of two unit vectors is sqrt3 then f...

    Text Solution

    |

  9. Find the equation of the plane if the point (5,-3,4) is the foot of th...

    Text Solution

    |

  10. Proved that the line (x-1)/2=(y+2)/(-3)=(z-3)/1 lies on the plane 7x+5...

    Text Solution

    |

  11. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

    Text Solution

    |

  12. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

    Text Solution

    |

  13. If A=[{:(1,2,0),(-2,-1,-2),(0,-1,1):}] then find A^-1 Using A^-1 solv...

    Text Solution

    |

  14. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

    Text Solution

    |

  15. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

    Text Solution

    |

  16. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  17. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

    Text Solution

    |

  18. Find the area enclosed by y^2=x^3,x=0,y=1

    Text Solution

    |

  19. Solve y^(2)+x^(2)dy/dx=xydy/dx.

    Text Solution

    |

  20. Prove the following by vector method. Altitudes of a triangle are conc...

    Text Solution

    |