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

`tan^(-1)(x/sqrt(a^2-x^2))=theta`
`tantheta=x/sqrt(a^2-x^2)`
`sintheta=x/a`
`theta=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. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

    Text Solution

    |

  2. Simplify sincot^(-1)tancos^(-1)x , x >0

    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. If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n the...

    Text Solution

    |

  5. If 2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is independent of x , then

    Text Solution

    |

  6. Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by

    Text Solution

    |

  7. If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has ...

    Text Solution

    |

  8. Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/...

    Text Solution

    |

  9. If Sn=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+ddotn terms, ...

    Text Solution

    |

  10. The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (...

    Text Solution

    |

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

    Text Solution

    |

  12. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a...

    Text Solution

    |

  13. If sin^(-1)x=2sin^(-1)alpha has a solution, then

    Text Solution

    |

  14. If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equ...

    Text Solution

    |

  15. The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...

    Text Solution

    |

  16. There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...

    Text Solution

    |

  17. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

    Text Solution

    |

  18. The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-pi/2)cot^(-1)...

    Text Solution

    |

  19. Each question contains statement given in two columns. Statement a,b...

    Text Solution

    |

  20. If x=sin^(-1)(a^6+1)+cos^(-1)(a^4+1)-tan^(-1)(a^2+1),a in R , then th...

    Text Solution

    |