Home
Class 12
MATHS
Prove that, 2 sin^(-1)x = sin^(-1) (2x s...

Prove that, `2 sin^(-1)x = sin^(-1) (2x sqrt (1-x^2))`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Solve 2 cos^(-1) x = sin^(-1) (2 x sqrt(1 - x^(2)))

Prove that 2cos^(-1)x=sin^(-1)(2xsqrt(1-x^2))

If x<0, then prove that cos^(-1)x=pi-sin^(-1)sqrt(1-x^2)

Prove that cos^(-1)x=2sin^(-1)(sqrt (1-x)/sqrt2)

prove that, 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2))) is constant

Prove that sin^(-1). ((x + sqrt(1 - x^(2)))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

UNITED BOOK HOUSE-SET 14-EXERCISE
  1. The S.D. of a binomial distribution with parameteres n and p is

    Text Solution

    |

  2. Let S = N xx Nand ast is a binary operation on S defined by (a,b)^**(c...

    Text Solution

    |

  3. Prove that, 2 sin^(-1)x = sin^(-1) (2x sqrt (1-x^2))

    Text Solution

    |

  4. prove without expanding, |[(a-b),1,a],[b-c,1,b],[c-a,1,c]|=|[a,1,b],[b...

    Text Solution

    |

  5. If two matrices A and B of orders 2 xxm and 3xxn respectively are conf...

    Text Solution

    |

  6. Evaluate:underset(xrarr0)lim log(1 + alphax)/(sin betax)

    Text Solution

    |

  7. If y = logxtanx, find (dy)/(dx).

    Text Solution

    |

  8. overset(pi//2)underset(-pi//2)int |sin x|dx =

    Text Solution

    |

  9. Form the diffential equation of family of parabolas having vertex at t...

    Text Solution

    |

  10. If f(x) = (x-1)e^x + 1, show that f(x) is positive for all positive va...

    Text Solution

    |

  11. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

    Text Solution

    |

  12. Find the equation of the plane which passing through the point hati + ...

    Text Solution

    |

  13. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

    Text Solution

    |

  14. A discrete random variable X has the following distribution: find a.

    Text Solution

    |

  15. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

    Text Solution

    |

  16. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  17. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

    Text Solution

    |

  18. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

    Text Solution

    |

  19. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

    Text Solution

    |

  20. Solve:(dy)/(dx)=(3x + 4y+1)/(-4x+2y-3)

    Text Solution

    |