Home
Class 12
MATHS
Prove that : tan^-1[(sqrt(1+x) - sqrt(1-...

Prove that : `tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/4 - 1/2cos^-1x`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^2))] = pi/4 - 1/2cos^-1x^2

Prove that tan^-1((sqrt(1+x)- (sqrt(1-x)))/(sqrt(1+x) + (sqrt(1-x)))) = pi/4 - 1/2 cos^-1 x

Prove that : tan^-1[(sqrt(1+z) + sqrt(1-z))/(sqrt(1+z) - sqrt(1-z))= pi/4 + 1/2 cos^-1z

Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqrt(1-sin x))] = x/2, x in (0, pi/4)

Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x

Show that : tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=pi/4+1/2cos^(-1)x^(2) .

Show that: tan^(-1)[(sqrt(1+x^(2)) + sqrt(1-x^(2)))/(sqrt(1 +x^(2))- sqrt(1-x^(2)))]=pi/4 +1/2 cos^(-1) x^(2), -1 lt x lt 1

Prove that 2 tan^-1 sqrt((1- x)/(1+x))= x, -1 le x le 1

Differentiate tan^(-1) ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) w.r.t. x .

PSEB-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise
  1. cos^-1 (cos frac{7pi}{6}) is equal to :

    Text Solution

    |

  2. sin (frac {pi}{3} - sin^-1 (-frac{1}{2})) is equal to:

    Text Solution

    |

  3. tan^-1 (sqrt3) -cot^-1 (-sqrt3) is equal to :

    Text Solution

    |

  4. cos^-1 (cos 13 pi/6) is :

    Text Solution

    |

  5. Find the value of the following: tan^-1(tan(7pi/6))

    Text Solution

    |

  6. Prove that : 2sin^-1 (3/5) = tan^-1 (24/7)

    Text Solution

    |

  7. Prove that : sin^-1 (8/17) + sin^-1(3/5) = tan^-1 (77/36)

    Text Solution

    |

  8. Prove that : cos^-1 (4/5) + cos^-1(12/13) = cos^-1 (33/65)

    Text Solution

    |

  9. Show that cos^-1 frac{12}{13} + sin^-1 frac {3}{5}= sin^-1 frac {56}{6...

    Text Solution

    |

  10. Prove that : sin^-1 (5/13) +cos^-1 (3/5) =tan^-1 (63/16)

    Text Solution

    |

  11. tan^-1 frac{1}{5} + tan^-1 frac{1}{7} + tan^-1 frac {1}{3} + tan^-1 fr...

    Text Solution

    |

  12. Prove that tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]

    Text Solution

    |

  13. Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqr...

    Text Solution

    |

  14. Prove that : tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/...

    Text Solution

    |

  15. Prove that: (9pi/8) - (9/4)sin^-1(1/3) = (9/4)sin^-1(2sqrt2/3)

    Text Solution

    |

  16. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

    Text Solution

    |

  17. Solve the following equation : tan^-1((1-x)/(1+x)) = (1/2)tan^-1x, (x>...

    Text Solution

    |

  18. sin(tan^-1x), |x|<1 is equal to :

    Text Solution

    |

  19. If sin^-1(1-x) - 2sin^-1x = pi/2, then x is equal to :

    Text Solution

    |

  20. tan^-1(x/y)-tan^-1((x-y)/(x+y)) is equal to :

    Text Solution

    |