Home
Class 12
MATHS
If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin...

If `tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n` the value of `sin^(-1)2x` is `6-2pi` (b) `2pi-6` `pi-3` (d) `3-pi`

A

`6-2pi`

B

`2pi-6`

C

`pi-3`

D

`3-pi`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin^(1)4)=(pi)/(2)`
`impliestan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+14-4pi)=(pi)/(2)`
`impliesx^(2)+3|x|-4=14impliesx^92)+6|x|-3|x|-18=0`
`(|x|+6)((|x|-3)=0,impliesx=+-3`
So, `sin^(-1)sin2x=sin^(-1)sin6` or `sin^(-1)sin(-6)=6-2pi` or `2pi-6`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n the value of sin^(-1)sin2x is (a) 6-2pi (b) 2pi-6 (c) pi-3 (d) 3-pi

The value of sin^(-1)(-sqrt(3)//2)\ is- a. -pi//3 b. -2pi//3 c. 4pi//3 d. 5pi//3

sin^(2) (pi/6)+cos^(2) (pi/3)-tan^(2) (pi/4)=-1/2

The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. -(3pi)/2

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to pi/2 (b) -pi (c) pi (d) -pi/2

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to pi/2 (b) -pi (c) pi (d) -pi/2

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to a) pi/2 (b) -pi (c) pi (d) -pi/2

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0 ,where theta in (-pi,pi], then the value of theta is (a) +-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2

If sin^(-1)(tan(pi/4))-sin^(-1)(sqrt(3/y))-(pi)/6=0 and x^(2)=y then x is equal to

If x in ( - pi/2, pi/2) , then the value of tan^(-1) ((tan x)/4) + tan^(-1) ((3 sin 2x)/(5 + 3 cos 2x)) is

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n th...

    Text Solution

    |

  2. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x + tan x and f si the inverse of g, then g'(x) equals

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. The function f(x) = (x^(2) - 1)|x^(2) - 3x + 3|+cos (|x|) is not diffe...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

    Text Solution

    |

  15. The sum of the roots of the equation tan^(-1)(x+3)-tan^(-1)(x-3)="sin"...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

    Text Solution

    |