Home
Class 12
MATHS
If 0 < cos^-1(x) <1 and 1+sin(cos^(-1)x...

If `0 < cos^-1(x) <1` and ` 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(-1)x) ` + ..... =2 then the value of 12 x^2 is____

Text Solution

Verified by Experts

The correct Answer is:
9
`1 + sin (cos^(-1) x) + sin^(2) (cos^(-1) x) + ...oo = 2`
`rArr (1)/(1-sin (cos^(-1)x)) = 2`
or `(1)/(2) = 1 - sin (cos^(-1) x)`
or `sin (cos^(-1)x) = (1)/(2)`
or `sin (cos^(-1) x) = (1)/(2)`
or `cos^(-1) x = (pi)/(6)`
or `x = (sqrt3)/(2) " or " 12x^(2) = 9`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

Similar Questions

Explore conceptually related problems

If A =[{:(2,0,0),(0,3,0),(0,0,5):}] , prove that, A^(2)=[{:(2^(2),0,0),(0,3^(2),0),(0,0,5^(2)):}] , hence by induction method show that, A^(n)=[{:(2^(n),0,0),(0,3^(n),0),(0,0,5^(n)):}]

Verify that the matrix equation A^2 - 4a +3I =0 is satisfied by the matrix A = [[2,-1],[-1,2]] , where I = [[1,0],[0,1]] and 0= [[0,0],[0,0]] ,

Verify that the matrix equation A^(2)-4A+3I = 0 is satisfied by the matrix A={:[(2,-1),(-1,2)]," where " I={:[(1,0),(0,1)]and 0={:[(0,0),(0,0)]. Hence obtain A^(-1).

If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], then =(|adj(adjA)|)/(2|adjA|) is equal to

If A = [[3,1],[-1,2]],I= [[1,0],[0,1]] and O = [[0,0],[0,0]] show that A^2-5A+7I=0 . Hence find A^(-1) .

If [1 0 0 0 1 0 0 0 1][x y z]=[1-1 0] , find x ,\ y\ a n d\ z .

If |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

If f(0) = 0 ,f'(0) = 2 , then the value differentiable at x = 0 of function y = f[f{f(x)}] is _

If a circle passes through the point (0,0),(a ,0)a n d(0, b) , then find its center.

If A = [{:(1,0,1),(0,1,2),(0,0,4):}] , then show that |3A|=27|A|.

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The number of values of x for which sin^(-1)(x^2-(x^4)/3+(x^6)/9...)+c...

    Text Solution

    |

  2. If the domain of the function f(x) = sqrt(3 cos^(-1) (4x) - pi) is [a,...

    Text Solution

    |

  3. If 0 < cos^-1(x) <1 and 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(...

    Text Solution

    |

  4. If tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(-1) (6/x ) then the value of x...

    Text Solution

    |

  5. If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], th...

    Text Solution

    |

  6. The number of roots of the equation is x^2 -7x+12=0

    Text Solution

    |

  7. If the area enclosed by the curves f(x) = cos^(-1) (cos x) and g(x) = ...

    Text Solution

    |

  8. Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sq...

    Text Solution

    |

  9. The least value of (1+sec^(-1)x)(1+cos^(-1)x) is

    Text Solution

    |

  10. Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot If x satisfies the e...

    Text Solution

    |

  11. The number of integral values of x satisfying the equation tan^(-1) (3...

    Text Solution

    |

  12. Number of solutions of equation sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x...

    Text Solution

    |

  13. If the equation sin^(-1)(x^2+x+1)+cos^(-1)(lambda x+1)=pi/2 has exactl...

    Text Solution

    |

  14. sin{2(sin^(-1)(sqrt(5))/3-cos^(-1)(sqrt(5))/3)} is equal to (ksqrt(5)...

    Text Solution

    |

  15. The number of solutions of "cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c...

    Text Solution

    |

  16. If x, y , z are in A.P and tan^-1 x , tan^-1 y and tan^-1 z are also ...

    Text Solution

    |

  17. Let, tan^-1y=tan^-1x+tan^-1((2x)/(1-x^2)), where absx lt 1/sqrt3. Then...

    Text Solution

    |

  18. The value of cot(sum(n=1)^(23)cot^-1(1+sum(k=1)^n2k)) is

    Text Solution

    |

  19. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

    Text Solution

    |

  20. For any positive integer n , define fn :(0,oo)rarrR as fn(x)=sum(j=1...

    Text Solution

    |