Home
Class 12
MATHS
Evaluate tan ^ (-1) {sin (-pi/2)}...

Evaluate ` tan ^ (-1) {sin (-pi/2)}`

Text Solution

Verified by Experts

`tan^{-1} (sin(frac{-pi}{2}))`
`=tan ^{-1} (-sin (frac{pi}{2}))`
`=tan ^{-1}(-1)=-frac{pi}{4}`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos
  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

Find the principal value of tan^(-1){sin(-(pi)/(2))}

Find the value of: i) sin ^(-1)(sin (3pi)/5) , ii) cos^(-1)(cos(13pi)/6) , iii) tan^(-1)(tan (7pi)/6) .

Evaluate the following (i) sin ( pi/2 - sin^(-1) ( (-1)/2)) (ii) sin(pi/2 - sin^(-1)(- sqrt3/2))

Evaluate the principal value of   v = tan^(-1)[sin(-(pi)/(2))] is:

Find the value of: i) sin^(-1)(sin (2pi)/3)) , ii) cos^(-1)(cos(7pi)/6) , iii) tan^(-1)(tan(3pi)/4)

Find the value of tan^(-1)(tan'(2pi)/(3)) .

Find the value of tan^(-1)(-1/(sqrt(3)))+cot^(-1)((1)/(sqrt(3))) + tan^(-1)[sin'((-pi)/(2))] .

Evaluate: tan{2tan-1(1)/(5)-(pi)/(4)}

Show that sin ^ (- 1) ((sin (3 pi)) / (7)) + cos ^ (- 1) ((cos (46 pi)) / (7)) + tan ^ (- 1) (- (tan (13 pi)) / (8)) + cot ^ (- 1) (cot (- (19 pi) / (8))) = (13 pi) / (7)

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Find the principal value of cos^(-1){sin"{"cos^(-1)1/2")"}

    Text Solution

    |

  2. If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then...

    Text Solution

    |

  3. Evaluate tan ^ (-1) {sin (-pi/2)}

    Text Solution

    |

  4. For the principal values, evaluate each of the following: tan^(-1){2co...

    Text Solution

    |

  5. For the principal values, evaluate each of the following: tan^(-1)sqr...

    Text Solution

    |

  6. Find the domain of sec^(-1)(3x-1) + sec^(-1)x-tan^(-1)x

    Text Solution

    |

  7. Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(...

    Text Solution

    |

  8. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

    Text Solution

    |

  9. Prove the following: 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)=pi/4 ...

    Text Solution

    |

  10. Evaluate: tan{1/2cos^(-1)(sqrt5/3)}

    Text Solution

    |

  11. sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to (A) 0,1/2 (B) 1,1...

    Text Solution

    |

  12. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

    Text Solution

    |

  13. Evaluate: tan(2tan^(-1)(1/5))

    Text Solution

    |

  14. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

    Text Solution

    |

  15. Show that: cos(2tan^(-1)(1/7))=sin(4tan^(-1)(1/3))

    Text Solution

    |

  16. Find the value of expression: sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2)...

    Text Solution

    |

  17. Find the principal value of each of the following: (i)sin^(-1)1/2-2s...

    Text Solution

    |

  18. If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/...

    Text Solution

    |

  19. Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

    Text Solution

    |

  20. Find the domain of f(x)=sin^(-1)x+cosxdot

    Text Solution

    |