Home
Class 12
MATHS
Find tan^(-1)x/(sqrt(a^2-x^2)) in terms ...

Find `tan^(-1)x/(sqrt(a^2-x^2))` in terms of `sin^(-1)` where `x in (0, a)dot`

Text Solution

Verified by Experts

We have `tan^(-1) (x)/(sqrt(a^(2) - x^(2))) = theta`
From the triangle,
`tan^(-1) (x)/(sqrt(a^(2) - x^(2))) = sin^(-1) (x)/(a)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then

Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)x/a ,-a lt x lt a

tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x)) where x!=0, is equal to

Find the domain of f(x)=sin^(-1)((x^2)/2)dot

If u = tan^(-1)"" (sqrt ( 1+x^2)-1)/(x) and v = tan^(-1) x , find (du)/(dv)

Find the range of f(x)=sqrt((cos^(-1)sqrt((1-x^2))-sin^(-1)x))

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

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to 0 (b) 2pi (c) pi (d) none of these

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

    Text Solution

    |

  2. Write tan^(-1) x, x gt 0 in the form of other inverse trigonometric fu...

    Text Solution

    |

  3. Find tan^(-1)x/(sqrt(a^2-x^2)) in terms of sin^(-1) where x in (0, a)d...

    Text Solution

    |

  4. Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

    Text Solution

    |

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

    Text Solution

    |

  6. Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

    Text Solution

    |

  7. Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)x/a ,-a<x<adot

    Text Solution

    |

  8. Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/4+(cos^(-1)x)/2,""0 <...

    Text Solution

    |

  9. Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x lt oo

    Text Solution

    |

  10. If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

    Text Solution

    |

  11. If (1)/(sqrt2) lt x lt 1, then prove that cos^(-1) x + cos^(-1) ((x + ...

    Text Solution

    |

  12. Find the value of sin^(-1)(sin5)+cos^(-1)(cos10)+tan^(-1){tan(-6)}+cot...

    Text Solution

    |

  13. Find the minimum value of the function f(x)=(pi^2)/(16cot^(-1)(-x))-co...

    Text Solution

    |

  14. Find the range of y=(cot^(-1)x)(cot^(-1)(-x))dot

    Text Solution

    |

  15. Prove that 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot

    Text Solution

    |

  16. Prove that : cos [ tan^(-1) { sin (cot^(-1) x)}]= sqrt((x^2 +1)/(...

    Text Solution

    |

  17. If sin^(-1)x=pi/5,forsom ex in (-1,1), then find the value of cos^(-1)...

    Text Solution

    |

  18. If sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1, then find the value of x.

    Text Solution

    |

  19. solve sin^(-1) x le cos^(-1) x

    Text Solution

    |

  20. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

    Text Solution

    |