Home
Class 12
MATHS
Find the value of x for which function a...

Find the value of `x` for which function are identical. `f(x)=tan^(-1)x+tan^(-1)1/x a n dg(x)=sin^(-1)x+cos^(-1)x`

Text Solution

Verified by Experts

The correct Answer is:
`[0, pi//2) uu {2pi]`
Let us draw the graph of both th efunction for `x in [0, 2pi]`

In the above figure, graph of `y = f (x) and y = g (x)` coincide for `x in [0,pi//2) uu {2pi}`
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

Find the value of x for which function are identical. f(x)=xa n dg(x)=1/(1//x)

Find the values of x for which the following pair of functions are identical. (i) f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x (ii) f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)

Find the value of x for which function are identical. f(x)=cosxa n dg(x)=1/(sqrt(1+tan^2x))

Find the value of x for which function are identical. f(x)=cosxa n dg(x)=1/(sqrt(1+tan^2x))

Which of the following pairs of functions is/are identical? (a) f(x)="tan"(tan^(-1)x)a n dg(x)="cot"(cot^(-1)x) (b) f(x)=sgn(x)a n dg(x)=sgn(sgn(x)) (c) f(x)=cot^2xdotcos^2xa n dg(x)=cot^2x-cos^2x (d) f(x)=e^(lnsec^(-1)x)a n dg(x)=sec^(-1)x

Find the value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

Find the value of x for which sin^(-1) (cos^(-1) x) lt 1 and cos^(-1) (cos^(-1) x) lt 1

Find the real values of x for which the function f(x) = cos^(-1) sqrt(x^(2) + 3 x + 1) + cos^(-1) sqrt(x^(2) + 3x) is defined

f(x)=tan^(-1)x+tan^(-1)(1/x);g(x)=sin^(-1)x+cos^(-1)x are identical functions if

Find the number of solution of the eqution tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)(3x)

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. solve sin^(-1) (sin 5) gt x^(2) - 4x

    Text Solution

    |

  2. Consider function f(x) = sin^(-1) (sin x) + cos^(-1) (cos x), x in [0,...

    Text Solution

    |

  3. Find the value of x for which function are identical. f(x)=tan^(-1)x+t...

    Text Solution

    |

  4. Express sin^(-1).(sqrtx)/(sqrt(x + a)) as a function of tan^(-1)

    Text Solution

    |

  5. If tan(cos^(-1) x) = sin (cot^(-1).(1)/(2)), then find the value of x

    Text Solution

    |

  6. Prove that: cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt...

    Text Solution

    |

  11. y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

    Text Solution

    |

  12. If x lt 0, the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (p...

    Text Solution

    |

  13. Find the value of tan^(-1) (-tan.(13pi)/(8)) + cot^(-1) (-cot((19pi)/(...

    Text Solution

    |

  14. If sin^(-1)x+sin^(-1)y=(2pi)/(3)",then"cos^(-1)x+cos^(-1)y is equal to

    Text Solution

    |

  15. Show that sin^-1 x+cos^-1 x=pi/2.

    Text Solution

    |

  16. If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5 pi^2) /8 find x.

    Text Solution

    |

  17. Solve tan^(-1) x gt cot^(-1) x

    Text Solution

    |

  18. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

    Text Solution

    |

  19. If alpha in (-(pi)/(2), 0), then find the value of tan^(-1) (cot alpha...

    Text Solution

    |

  20. Find the maximum value of (sec^(-1) x) (cosec^(-1) x), x ge 1

    Text Solution

    |