Home
Class 12
MATHS
If 0 lt phi lt (pi)/(2) , x= sum(n=0)...

If `0 lt phi lt (pi)/(2) , x= sum_(n=0)^(oo) cos^(2n) phi ,y sum _(n=0)^(oo) sin ^(2n) phi and z = sum _(n=0) ^(oo) cos ^(2n) phi sin ^(2n) phi , ` then

A

HP

B

Arithmetric - Geometric progression

C

AP

D

GP

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|49 Videos
  • RELATIONS AND FUNCTIONS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|33 Videos
  • SETS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|21 Videos

Similar Questions

Explore conceptually related problems

If x = sum_(n = 0)^(infty) cos ^(2n) theta, " "y = sum_(n = 0)^(infty) sin^(2n) theta and z = sum_(n = 0)^(infty) cos^(2n) theta sin^(2n)theta, 0 lt theta lt (pi)/(2) , then show that xyz = x + y + z [ Hint : use the formula 1 + x + x^(2) + x^(3) +... =(1)/(1 - x) , where |x| lt 1 ]

If xsum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)thetaandz=sum_(n=0)^(oo)cos^(2n)thetasin^(2n)theta,ltthetalt(pi)/(2), then show that xyz = x + y + z.

Find sum_(n=1)^(oo)1/(n^2+5n+6)

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

If the sum of the series sum_(n=0)^oor^n ,|r|<1 is s , then find the sum of the series sum_(n=0)^oor^(2n) .

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

The expression sum_(n=1)^(oo)cot^(-1)(n^(2)-3n+3) simplifies to

NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
  1. if 1,log(9)(3^(1 - x) + 2),log(3)[4.3^(x) - 1] are in A.P. then x equa...

    Text Solution

    |

  2. 1^(3) - 2^(3) + 3^(3) + 4^(3) + .... + 9^(3) =

    Text Solution

    |

  3. Sum of infinite number of terms in GP is 20 and sum of their square is...

    Text Solution

    |

  4. The value of 2^(1/4), 4^(1/8), 8^(1/16) ...... infty is

    Text Solution

    |

  5. Fifth term of a GP is 2, then the product of 1ts 9 terms is

    Text Solution

    |

  6. If the system of linear equations x + 2ay + az = 0,x + 3by + bz = 0,x ...

    Text Solution

    |

  7. Let f(x) be a polynomial function of second degree. If f(1) = f(-1) an...

    Text Solution

    |

  8. The sum of the series 1/1.2 - 1/2.3 + 1/3.4 … upto infty is equal to

    Text Solution

    |

  9. If x(1),x(2),x(3)as well as y(1),y(2),y(3) are in geometric progressio...

    Text Solution

    |

  10. Let T, be the r^(th) term of an A.P. whose first term is a and common ...

    Text Solution

    |

  11. The sum of first n terms of the series 1(2) + 2.2^(2) + 3^(2) + 2.4^(2...

    Text Solution

    |

  12. The sum of series 1/2! + 1/4! + 1/6! + …….. is

    Text Solution

    |

  13. If the coefficients of r^(th),(r + 1)^(th) and (r + 2)^(th) terms in t...

    Text Solution

    |

  14. If 0 lt phi lt (pi)/(2) , x= sum(n=0)^(oo) cos^(2n) phi ,y sum (n...

    Text Solution

    |

  15. If a(1), a(2), a(3), ………, a(n)….. are in G.P., then the determinant De...

    Text Solution

    |

  16. Leta(1), a(2), a(3), ………be terms of an A.P. if (a(1) + a(2) + ...... a...

    Text Solution

    |

  17. If a(1), a(2) , ……. A(n) are in H.P., then the expression a(1)a(2) + a...

    Text Solution

    |

  18. The sum of the series 1/(2!) - 1/(3!) + 1/(4!) - …….. upto infinity is

    Text Solution

    |

  19. In a geometric progression consisting of positive terms each term equa...

    Text Solution

    |

  20. The first two terms of a geometric progression add up to 12. The su...

    Text Solution

    |