Home
Class 12
MATHS
Show that sin^(-1)(2xsqrt(1-x^(2)))=2cos...

Show that `sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x, (1)/(sqrt2)le x le 1.`

Text Solution

Verified by Experts

The correct Answer is:
`LHS = RHS`
Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAM QUESTION PAPER MARCH - 2016

    SUNSTAR PUBLICATION|Exercise PART - C (Answer any ten questions)|28 Videos

  • ANNUAL EXAM QUESTION PAPER MARCH - 2016

    SUNSTAR PUBLICATION|Exercise PART - D (Answer any six questions)|24 Videos

  • ANNUAL EXAM QUESTION PAPER MARCH - 2016

    SUNSTAR PUBLICATION|Exercise PART - E (Answer any one questions)|8 Videos

  • ANNUAL EXAM QUESTION PAPER MARCH -2014

    SUNSTAR PUBLICATION|Exercise PART-E|4 Videos

Similar Questions

Explore conceptually related problems

Show that sin^(-1)(2xsqrt(1-x^(2))) = 2sin^(-1)x ,

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

y = sin^(-1)(2xsqrt(1 - x^2)), -1/(sqrt2) lt x lt 1/(sqrt2)

If y = sin^(-1) (2xsqrt(1-x^(2))) + sec^(-1) (1/sqrt(1-x^(2))) then dy/dx =

If cos^(-1)x=alpha, (0 lt x lt 1) and sin^(-1)(2x sqrt(1-x^(2)))+sec^(-1)((1)/(2x^(2)-1))=(2pi)/(3) , then tan^(-1)(2x) equals

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1

SUNSTAR PUBLICATION-ANNUAL EXAM QUESTION PAPER MARCH - 2016-PART - B (Answer any ten questions)
  1. Evaluate : int(0)^(pi) ( sin^(2) ((x)/(2) ) - cos^(2) ( (x)/(2) ))dx

    Text Solution

    |

  2. If |overset(to)(a) + overset(to)(b)| =| overset(to)(a) - overset(to)(b...

    Text Solution

    |

  3. Find the order and degree, if defined, of the differential equation. ...

    Text Solution

    |

  4. Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(...

    Text Solution

    |

  5. The random variable X has probability distribution P(X) of the followi...

    Text Solution

    |

  6. Find the Cartesian equation of the line parallel to y - axis and passi...

    Text Solution

    |

  7. Write the simplest form of tan^(-1) [( 3 cos x - 4 sin x )/( 4 cos x +...

    Text Solution

    |

  8. Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c...

    Text Solution

    |

  9. If functions f : R to R and g: R to R are given by f(x) = |x| and g(x)...

    Text Solution

    |

  10. Show that sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x, (1)/(sqrt2)le x le 1.

    Text Solution

    |

  11. Find (dy)/(dx) if y= sec^(-1)((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2))

    Text Solution

    |

  12. If x^(y) = a^(x), prove that (dy)/( dx) = ( x log (e) a -y)/( x log(e)...

    Text Solution

    |

  13. Find int (1)/( sin x cos^(3) x) dx

    Text Solution

    |

  14. Using differentials find the approximate value of (25)^(1//3)

    Text Solution

    |

  15. Evaluate : int(0)^(pi) ( sin^(2) ((x)/(2) ) - cos^(2) ( (x)/(2) ))dx

    Text Solution

    |

  16. If |overset(to)(a) + overset(to)(b)| =| overset(to)(a) - overset(to)(b...

    Text Solution

    |

  17. Find the order and degree, if defined, of the differential equation. ...

    Text Solution

    |

  18. Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(...

    Text Solution

    |

  19. The random variable X has probability distribution P(X) of the followi...

    Text Solution

    |

  20. Find the Cartesian equation of the line parallel to y - axis and passi...

    Text Solution

    |