Home
Class 12
MATHS
For 0 lt theta lt ( pi )/(2) , if x = su...

For `0 lt theta lt ( pi )/(2) `, if `x = sum_(n=0)^(oo)cos^(2n) theta, y = sum_(n=0)^(oo) sin^(2n) theta ,z=sum_(n=0)^(oo)cos^(2n) theta sin^(2n) theta`,then `:`

A

`xyz=xz+y`

B

`xyz=xy+z`

C

`xyz=x+y+z`

D

`xyz=yz+x`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise LATEST QUESTIONS|11 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • RELATIONS

    MODERN PUBLICATION|Exercise RCQS|6 Videos

  • SETS

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|6 Videos

Similar Questions

Explore conceptually related problems

If x = sum_(n=0)^(oo) a^(n) .,y=sum_(n=0)^(oo) b^(n) , z = sum_(n=0)^(oo) (ab)^(n) , where a,blt 1 , then :

If s= sum_(n=0)^(oo) a^(n) , y = sum_(n=0)^(oo) b^(n) , z= sum _(n=0)^(oo) c^(n) , where a, b c are in A.P. and |a| lt 1, |b|lt 1 , |c| lt 1 then x,y,z are in :

For 0ltphilepi//2 , if : x=underset(n=0)overset(oo)sumcos^(2n)phi,y=underset(n=0)overset(oo)sumsin^(2n)phi , z=underset(n=0)overset(oo)sumcos^(2n)sin^(2n)phi , then :

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .

(sin^(2) theta)/(1-cos theta)-(cos^(2) theta)/(1-sin theta)=cos theta-sin theta

If ((1+cos theta+i sin theta)/(sin theta+i+i cos theta))^(4)=cos n theta+i sin n theta , then n=

If 0 lt theta lt (pi)/(2) and tan theta+sec theta=p then sec theta=

lim_(n rarr oo) (sin n theta)/(sqrt n) =

lim_(n rarr oo) 1/n^(3) sum_(k=1)^(n) k^(2)x =

MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)...

    Text Solution

    |

  2. If x(1), x(2),"……….",x(n) are n non zero real numbers such that (x(1)^...

    Text Solution

    |

  3. For 0 lt theta lt ( pi )/(2) , if x = sum(n=0)^(oo)cos^(2n) theta, y =...

    Text Solution

    |

  4. If a(1), a(2) ,a(3)"….." is an A.P. such that : a(1) + a(5) + a(10)+...

    Text Solution

    |

  5. If f(x) is a function satisfying f(x+y) = f(x) f(y) for all x,yin N su...

    Text Solution

    |

  6. If sin alpha, sin^(2) alpha, 1,sin^(4) alpha, sin^(5) alpha, ( - pi lt...

    Text Solution

    |

  7. If A,G and H are respectively A.M.,G.M. and H.M. of three positive num...

    Text Solution

    |

  8. x+y+z = 15 if 9, x,y,z,a are in A.P., while (1)/( x) + ( 1)/( y) + ( ...

    Text Solution

    |

  9. If p,q,r are in A.P. and are positive, the roots of the quadratic equa...

    Text Solution

    |

  10. Let a^(n) be the nth term of the G.P. of positive numbers. Let sum(n=1...

    Text Solution

    |

  11. Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N ...

    Text Solution

    |

  12. For any odd integer n ge1, n^(3) - ( n - 1)^(3) + "….." + ( -1)^(n-1)1...

    Text Solution

    |

  13. The sum to infinity of the series : 1+2 ( 1-(1)/( n )) + 3( 1 - ( 1)...

    Text Solution

    |

  14. If a,b,c are digits, then the rational number represented by 0.c ab ab...

    Text Solution

    |

  15. If I(n) = int(0)^(n) ( 1- sin 2nx)/( 1-cos 2n)dx then I(1) , I(2) , I(...

    Text Solution

    |

  16. If p,q,r , three positive real numbers are in A.P., then the roots of ...

    Text Solution

    |

  17. If a(1),a(2) , a(3),"……..",a(n) are in H.P. , then : (a(1))/( a(2) ...

    Text Solution

    |

  18. The value of sum(r=1)^(n) log ((a^(r ))/( b^(r-1))) is :

    Text Solution

    |

  19. If a(1) , a(2),"………",a(n) are n non-zero real numbers such that ( a(1)...

    Text Solution

    |

  20. The sum of n terms of the series : (1)/( 1.2.3.4) + ( 1)/( 2.3.4.5) ...

    Text Solution

    |