Home
Class 12
MATHS
If a(r+1)=sqrt(1/2 ( 1+a(r))), the prove...

If `a_(r+1)=sqrt(1/2 ( 1+a_(r)))`, the prove that
`cos((sqrt(1-a_(0)^(2)))/(a_(1)*a_(2)*a_(3)... "to" oo))=a_(0)` .

A

1

B

`-1`

C

`a_(0)`

D

`1//a_(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) -a_(2))^(2) = (a_(1)-a_(4))^(2)

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)-a_(1)++a_(2)-a_(3)+……+a_(20)=4^(10)

if a_(r) = (cos 2r pi + I sin 2 r pi)^(1//9) then prove that |{:(a_(1),,a_(2),,a_(3)),a_(4) ,,a_(5),,a_(6)),( a_(7),, a_(8),,a_(9)):}|=0

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_(1),a_(2),a_(3),….,a_(r) are in GP, then prove that the determinant |(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(4+15)),(a_(r+11),a_(r+17),a_(r+21))| is independent of r .

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(i) gt 0 (i = 1,2,3,….n) prove that sum_(1 le i le j le n) sqrt(a_(i)a_(j)) le (n - 1)/(2) (a_(1) + a_(2) + …. + a_(n))

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
  1. If x(1),x(2),x(3),...,x(n) are in A.P. whose common difference is alph...

    Text Solution

    |

  2. If asin^2x+bcos^2x=c,bsin^2y+acos^2y=d and atanx=btany then a^2/b^2=.....

    Text Solution

    |

  3. If a(r+1)=sqrt(1/2 ( 1+a(r))), the prove that cos((sqrt(1-a(0)^(2))...

    Text Solution

    |

  4. If alpha,beta,gamma,delta are the smallest positive angles in ascendin...

    Text Solution

    |

  5. The value of cos y cos (pi/2-x)-cos (pi/2 - y) cos x + sin y cos (pi/2...

    Text Solution

    |

  6. If cosx-sinalphacotbetasinx=cosa , then the value of tan(x/2) is -tan(...

    Text Solution

    |

  7. The expression cosec^(2)A cot^(2)A-sec^(2)A tan^(2)A-(cot^(2)A-tan^(...

    Text Solution

    |

  8. If sin alpha -cos alpha = m, then the value of sin^6alpha+cos^6alpha i...

    Text Solution

    |

  9. The value of x , 0 le x le (pi)/2 which satisfy the equation 81^( si...

    Text Solution

    |

  10. If cos(A-B)=3/5 and tan A tan B=2, then (a) cos Acos B=1/5 (b) sin A ...

    Text Solution

    |

  11. The value of (3+cot76^@cot16^@)/(cot76^@+cot16^@) is

    Text Solution

    |

  12. If sin x+sin^(2)x=1, " then " cos^(8)x+2 cos^(6)x+cos^(4)x=

    Text Solution

    |

  13. If a=b cos((2pi)/3)= c cos((4pi)/3), then write the value of a b+b c+c...

    Text Solution

    |

  14. If sinα.sinβ−cosα.cosβ+1=0 then show that 1+cotα.tanβ=0

    Text Solution

    |

  15. If sintheta(1)+sintheta(2)+sintheta(3)=3, then cos theta(1)+cos theta(...

    Text Solution

    |

  16. If A lies in the third quadrant and 3 tan A-4 = 0, then 5 sin 2A + 3si...

    Text Solution

    |

  17. tan 5x tan3x tan2x=

    Text Solution

    |

  18. The value of sin12^(@)sin24^(@)sin48^(@)sin84^(@), is

    Text Solution

    |

  19. If A+B+C=(3pi)/2, t h e ncos2A+cos2B+cos2C is equal to 1-4cos Acos Bc...

    Text Solution

    |

  20. If A+C=B,then tanA tanBtanC=

    Text Solution

    |