Home
Class 11
MATHS
If x in (0,pi//2)a n dcosx=1//3 , then p...

If `x in (0,pi//2)a n dcosx=1//3` , then prove that `sum_(n=0)^oo(cosn x)/(3^n)=(3(3-cosx))/(10-6cosx+cos^2x)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

To prove (cos5x+cos4x)/(1-2cos3x) = -cos2x-cosx

Solve cosx+cos3x-2cos2x=0

Solve: cos3x+cosx-cos2x=0

Prove that sum_(r = 0)^n r^3 . C_r = n^2 (n +3).2^(n-3)

The value of the sum_(n=0)^oo(2n+3)/(3^n) is equal to_________.

Solve cos3x+cosx-cos2x=0

If t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3, then prove that (3tanx-t a n^3x)/(1-3t a n^2x)=1 .

value of lim_(x->0)(1-cos^3x)/(xsinx*cosx) is

Find the sum sum_(n=1)^(oo)(6^(n))/((3^(n)-2^(n))(3^(n+1)-2^(n+1)))

Prove that 3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

    Text Solution

    |

  2. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  3. If x in (0,pi//2)a n dcosx=1//3 , then prove that sum(n=0)^oo(cosn x)/...

    Text Solution

    |

  4. Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real value...

    Text Solution

    |

  5. Let Zp=rp(costhetap+isinthetap),p=1,2,3a n d1/(Z1)+1/(Z2)+1/(Z3)=0. Co...

    Text Solution

    |

  6. Find the least value of ((6x^2-22 x+21))/((5x^2-18x+17)) for real xdot

    Text Solution

    |

  7. Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' ...

    Text Solution

    |

  8. Find the range of the function f(x)=x^2-2x-4.

    Text Solution

    |

  9. If x=9^(1/3) 9^(1/9) 9^(1/27) ...->∞ , y= 4^(1/3) 4^(-1/9) 4^(1/27) ....

    Text Solution

    |

  10. Find the linear factors of 2x^2-y^2-x+x y+2y-1.

    Text Solution

    |

  11. If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a)-sqrt(|a|b) (b...

    Text Solution

    |

  12. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

    Text Solution

    |

  13. The number of solutions of z^2+overlinez = 0 is

    Text Solution

    |

  14. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

    Text Solution

    |

  15. Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following comple...

    Text Solution

    |

  16. If x-c is a factor of order m of the polynomial f(x) of degree n (1 < ...

    Text Solution

    |

  17. If z1a n dz2 are two complex numbers such that |z1|=|z2|a n d arg(z1)+...

    Text Solution

    |

  18. Solve the equation x^3-13 x^2+15 x+189=0 if one root exceeds the other...

    Text Solution

    |

  19. Let z1, z2, z3 be the three nonzero complex numbers such that z2!=1,a=...

    Text Solution

    |

  20. If tantheta and sectheta are the roots of a x^2+b x+c=0, then prove th...

    Text Solution

    |