Home
Class 12
MATHS
Find the value of x for which sec^(-1)xs...

Find the value of `x` for which `sec^(-1)xsin^(-1)x=pi/2dot`

Text Solution

Verified by Experts

We know that `sec^(-1) x` is defined for `x in (-oo, -1] uu [1, oo)`. But `sin^(-1) x` is defined for `x in [-1, 1]`
Hence, `sec^(-1) x + sin^(-1) x = (pi)/(2) " for " x = +- 1`
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 sec^(-1)x+sin^(-1)x=pi/2dot

Solve sin^(-1)x+sin^(-1)2x=pi/3dot

Find the value of "cos"(2cos^(-1)x+sin^(-1)x) at x=1/5, where 0lt=pi and -pi/2lt=sin^(-1)xlt=pi/2dot

Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0,2pi)dot

Find the set of value of x for which the equation cos^(-1) x + cos^(-1) ((x)/(2) + (1)/(2) sqrt(3 -3x^(2))) = (pi)/(3) holds goods

Find the value of x for which the matrix A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)] is singular.

Find the value of x for which the following expression are defined (i) sin^(-1) (3x -2) (ii) cos^(-1) (log_(e) x) (iii) sec^(-1) (x^(2) -2)

Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)1/x+cos^(-1)1/ydot

Find the minimum value of (sec^(-1)x)^2+("c o s e c"^(-1)x)^2

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the value of sin^(-1)(2^x) (ii) cos^(-1)sqrt(x^2-x+1) tan^(-1)(...

    Text Solution

    |

  2. Find the range of f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot

    Text Solution

    |

  3. Find the value of x for which sec^(-1)xsin^(-1)x=pi/2dot

    Text Solution

    |

  4. If sin^(-1)(x^2+2x+2)+tan^(-1)(x^2-3x-k^2)>pi/2, then find the values ...

    Text Solution

    |

  5. If cos^(-1)lambdacos^(-1)mu+cos^(-1)gamma=3pi, then find the value of ...

    Text Solution

    |

  6. If sin^(-1)x1+sin^(-1)x2++sin^(-1)xnlt==(npi)/2,n in N ,n=2m+1, mgeq1...

    Text Solution

    |

  7. Find x satisfying [tan^(-1)x]+[cos^(-1)x]=2, where [] represents the g...

    Text Solution

    |

  8. If cos (2 sin^(-1) x) = (1)/(9), then find the value of x

    Text Solution

    |

  9. Find the value of sin(1/2cot^(-1)(-3/4))

    Text Solution

    |

  10. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

    Text Solution

    |

  11. Solve sin^(-1)(1-x)-2s in^(-1)x=pi/2

    Text Solution

    |

  12. Find the solutions of the equation cos(cos^-1 x) =cosec (cosec^-1x).

    Text Solution

    |

  13. Find the principal values of the following (i) sin^(-1) (sin 1) (ii...

    Text Solution

    |

  14. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

    Text Solution

    |

  15. Find the area bounded by y sin^(-1) (sin x) and x-axis for x in [0, 10...

    Text Solution

    |

  16. Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1)...

    Text Solution

    |

  17. Find the principal value of the following (i) cos^(-1) (cos 3) (ii) ...

    Text Solution

    |

  18. Solve cos^(-1) (cos x) gt sin^(-1) (sin x), x in [0, 2pi]

    Text Solution

    |

  19. Find tan^(-1) tan ((2pi)/3)

    Text Solution

    |

  20. Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

    Text Solution

    |