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

If `f(x)=[[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]]` , show that `f(x).f(y)=f(x+y)`

Promotional Banner

Topper's Solved these Questions

  • RELATION & FUNCTIONS

    JMD PUBLICATION|Exercise EXERCISE|21 Videos

  • VECTOR ALGEBRA

    JMD PUBLICATION|Exercise EXAMPLE|54 Videos

Similar Questions

Explore conceptually related problems

Let f(x)= [[cos x, -sin x, 0],[sin x, cos x, 0],[0,0,1]] ,Show that f (x) f(y)= f(x+y) .

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

Inverse of f(x) = [(cos x , sin x, 0),(-sin x, cos x, 0),(0,0,1)] is

Let f(x) = |{:(2cos ^(2) x,,sin 2x,,-sin x),(sin 2x,,2 sin^(2)x,,cos x),(sin x,,-cos x,,0):}| .then the value of int_(0)^(pi//2) [ f(x) +f'(x) ] dx " is "

If f(x) = |(sin x, cos x , tan x),(x^3, x^2 ,x),(2x, 1,x)| then Lim_(x to 0) (f(x))/(x^2) equals

if f(x) = (x-1)/(x+1), x ne -1 , then show that : f(f(x)) = -1/x, x ne 0 .

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f(x)-f(y) is equal to

If f'(x) = a sin x + b cos x and f'(0) = 4,f(0) = 3, f((pi)/(2))= 5 , find f(x).

If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not differentiable at x =0

JMD PUBLICATION-SOLVED SAMPLE QUESTION PAPERS-EXAMPLE
  1. State whether it is true or false:If A and B are dependent events then...

    Text Solution

    |

  2. Show that the points (a+5,a+4), (a-2,a+3) and (a,a) do not lie on a st...

    Text Solution

    |

  3. If f(x)=[[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]] , show that f(x).f(...

    Text Solution

    |

  4. The slope of the curve 2y^2-ax^2=b at (1,-1) is -1 find a and b.

    Text Solution

    |

  5. integrate int (cos2x-cos2alpha)/(cosx-cosalpha) dx

    Text Solution

    |

  6. solve 'int0^(π/4)sqrt(1+sin2xdx)'

    Text Solution

    |

  7. find the area of the region bounded by 'y^2=4x' and x=2

    Text Solution

    |

  8. Find lambda so that the scalar projection of veca=lambdahati+hatj+4hat...

    Text Solution

    |

  9. Find unit vector in the direction of veca+vecb, where veca=-hati+hatj+...

    Text Solution

    |

  10. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

    Text Solution

    |

  11. If x^y+y^x= (x+y)^(x+y), then prove that dy/dx= ((x+y)^(x+y) [1+log(x+...

    Text Solution

    |

  12. If y= [Log(x+sqrt(x^2+1))]^2 then show that (x^2+1)y2+xy1=0

    Text Solution

    |

  13. Evaluate intdx/(sinx-sin2x)

    Text Solution

    |

  14. Solve (3xy+y^2)dx+(x^2+xy)dy=0, y(1)=1

    Text Solution

    |

  15. solve the differential equation: dy/dx=tan(x+y)

    Text Solution

    |

  16. A car manufacturing factory has to plant s X and Y. Plan X manufacture...

    Text Solution

    |

  17. Solve the following system of linear equations by matrix method: x - y...

    Text Solution

    |

  18. If A= [[1,2,2,],[2,1,2,],[2,2,1,]] then verify A^-1A=I

    Text Solution

    |

  19. Find the shortest distance (S.D.) between the lines : vec r = hat i + ...

    Text Solution

    |

  20. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

    Text Solution

    |