Home
Class 11
MATHS
Value of cos^-1 sqrt((1 + sqrt(1 + x^2))...

Value of `cos^-1 sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))) , x ge 0` is

A

`tan^-1 x`

B

`1/2 tan^-1 x`

C

`cot^-1 x`

D

`1/2 cot^-1 x`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos

  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

show that , (1) /(2) tan ^(-1) x = cos^(-1) sqrt((1+sqrt(1+x^(2)))/(2sqrt(1+x^(2)))).

The value of cos^-1 x + cos^-1 {x/2 + sqrt3/2 cdot sqrt(1 - x^2)}, x gt 1/2 is

The value of sin^(-1)[xsqrt(1-x)+sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

If 2x = sqrt((a)/(b)) - sqrt((b)/(a)) , then show that (2a sqrt(1 + x^(2)))/(x + sqrt(1 + x^(2))) = a + b

If x = sqrt3/2 then find the value of (sqrt(1+x) - sqrt(1-x))/(sqrt(1+x) + sqrt(1-x))

When x = (sqrt3)/(2) , the value of ((1 + x)/(1 + sqrt1 + x) + (1- x)/(1 - sqrt1 - x)) is____

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. The value of tan (pi/4 + 1/2 cos^-1(2/3))+tan(pi/4 - 1/2 cos^-1 (2/3))...

    Text Solution

    |

  2. The value of cos^-1 x + cos^-1 {x/2 + sqrt3/2 cdot sqrt(1 - x^2)}, x g...

    Text Solution

    |

  3. Value of cos^-1 sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))) , x ge 0 is

    Text Solution

    |

  4. The value of tan^2 (sec^-1 2)+ cot^2(cosec^-1 3) is

    Text Solution

    |

  5. 2 cos^-1 x = sin^-1(2xsqrt(1 - x^2)) is valid for

    Text Solution

    |

  6. If 0 le x le 3pi , 0 le y le 3pi and cos x cdot sin y = 1 , then the p...

    Text Solution

    |

  7. The number of solution of the equation x^3 + x^2 + 4x + 2 sin x = 0 , ...

    Text Solution

    |

  8. The number of values of x in [0 , 4pi] satisfying abs(sqrt3 cos x - si...

    Text Solution

    |

  9. The number of solution (s) of the equation sin^4 x + cos^4 x = sinx co...

    Text Solution

    |

  10. Number of solution of (sin4theta)/(sin 2theta) = (y + 1)/(y - 1) if 1/...

    Text Solution

    |

  11. The number of values of x satisfying the equation sqrt(sin x) - 1/sqrt...

    Text Solution

    |

  12. The equation e^(sin x) -e^(-sin x)-4=0 has

    Text Solution

    |

  13. The number of solution of 2 sin x = 5x^2 + 2x + 3 is

    Text Solution

    |

  14. In 0 lt x lt 2pi , the no of solution (s) of the equation sin^3 x + co...

    Text Solution

    |

  15. The no. of solution(s) of the equation log(cosx) sinx + log(sinx) cosx...

    Text Solution

    |

  16. The set of real values of k for which x^2 - kx + sin^-1 (sin 4) gt 0 f...

    Text Solution

    |

  17. If 'alpha' satisfies the equation x^2 - x - 2 gt 0 , then which of the...

    Text Solution

    |

  18. The general solution of the equation : sum(r =1)^n cos(r^2 x) sin(r x)...

    Text Solution

    |

  19. The value of x between 0 and 2 pi which satisfy the equation sinxsqrt(...

    Text Solution

    |

  20. The solution set of inequality log(1/2) sin^-1 x gt log(1/2) cos^-1 x

    Text Solution

    |