Home
Class 12
MATHS
The value of sin^(-1)("cos"(cos^(-1)(cos...

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`

A

`(pi)/(2)`

B

`-pi`

C

`pi`

D

`-(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(-1) (cos (cos^(-1) (cos x) + sin^(-1) (sin x)))`
`= sin^(-1) (cos (x + pi - x)) " " ["as " x in (pi//2)]`
`= sin^(-1) (cos pi) = sin^(-1) (-1) = -(pi)/(2)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

Similar Questions

Explore conceptually related problems

Solve cos^(-1)(cosx)>sin^(-1)(sinx),x in [0,2pi]

The value of cos^(-1)("cos"(5pi)/(3))+sin^(-1)("sin"(5pi)/(3)) is -

The value of I=int_(0)^(pi)x(sin^(2)(sinx)+cos^(2)(cosx))dx is

If alpha in (0,pi/2) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)-cos^(-1)(cosalpha) is equal to (a) 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha

If |sin^(-1)x|+|cos^(-1)x|=pi/2,t hen

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

Solve cos2x >|sinx|,x in (pi/2,pi)

prove that sin^(-1) cos sin^(-1)x + cos^(-1) sin cos^(-1)x = pi /2

int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to (pi^2)/6 (b) (pi^2)/3 (c) (pi^2)/8 (d) (3pi^2)/8

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

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The value of sin^(-1)(sin12)+cos^(-1)(cos12)=

    Text Solution

    |

  2. The value of the expression sin^(-1)(sin(22pi)/7)+cos^(-1)(cos(5pi)/3)...

    Text Solution

    |

  3. The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x i...

    Text Solution

    |

  4. If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^...

    Text Solution

    |

  5. tan^-1[(cos x)/(1+sin x)] is equal to

    Text Solution

    |

  6. If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is const...

    Text Solution

    |

  7. If sin^(-1) : [-1, 1] rarr [(pi)/(2), (3pi)/(2)] and cos^(-1) : [-1, 1...

    Text Solution

    |

  8. Let ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If tan^(-1)((sqrt(1+x^2)-1)/x)=4^0 then (a)x=tan2^0 (b) x=tan4^0 (c)...

    Text Solution

    |

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

    Text Solution

    |

  13. tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b)...

    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. Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x...

    Text Solution

    |

  16. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

    Text Solution

    |

  17. lf asin^-1 x -bcos^-1 x=c,then asin^-1 x +bcos^-1 x equal to

    Text Solution

    |

  18. The solution set of inequality log(1/2) sin^-1 x gt log(1/2) cos^-1 x

    Text Solution

    |

  19. sin ^-1 ( sin θ ) > cos ^-1 ( sin θ ) find the range of θ

    Text Solution

    |

  20. If |sin^(-1)x|+|cos^(-1)x|=pi/2,t hen

    Text Solution

    |