Home
Class 12
MATHS
(9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(...

`(9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3)`
`(9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)`
`=(9)/(4)((pi)/(2)-sin^(-1)""(1)/(3))=(9)/(4)cos^(-1)""(1)/(3)`
`=(9)/(4)sin^(-1)""sqrt(q-((1)/(3))^(2)) " " ( :. cos^(-1)x=sin^(-1)sqrt(1-x^(2)))`
`=(9)/(4)sin^(-1)sqrt((8)/(9))=(9)/(4)sin^(-1)""((2sqrt(2))/(3))`=RHS Hence Proved.

Promotional Banner

Topper's Solved these Questions

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise Questions From NCERT Exemplar|4 Videos
  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 2 (a) (Short Answer Type Questions)|10 Videos
  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (2)|11 Videos
  • INTEGRALS

    MODERN PUBLICATION|Exercise COMPETITION FILE|24 Videos
  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise Chapter Test|12 Videos

Similar Questions

Explore conceptually related problems

Prove that: (9 pi)/(8)-(9)/(4)sin^(-1)(1)/(3)=(9)/(4)sin^(-1)(2sqrt(2))/(3)

Prove the following: (9)/(8)-(9)/(4)sin^(-1)((1)/(3))=(9)/(4)sin^(-1)((2sqrt(2))/(3))

Prove that: (9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2sqrt(2))/3)

" (4) "sin cos^(-1)(-(sqrt(3))/(2))

Prove (9 pi) / (8) - (9) / (4) sin ^ (- 1) ((1) / (3)) = (9) / (4) sin ^ (- 1) (2 (sqrt (2)) / (3))

sin^(-1){cot(sin^(-1)(sqrt((2-sqrt(3))/(4))+cos^(-1)((sqrt(12))/(4))+sec^(-1)sqrt(2))}

If A=9tan^(-1)(sqrt(2)-1) and B=3sin^(-1)((1)/(3))+sin^(-1)((3)/(5)) then

If sin^(-1)((sqrt(x))/2)+sin^(-1)(sqrt(1-x/4))+tan^(-1)y=(2pi)/3 , then

sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)(sqrt(2))= (a) 0 (b) pi/4 (c) pi/6 (d) pi/2

The value of ((4)/(9))^((1)/(3))-((2)/(9))^((1)/(3))+((1)/(9))^((1)/(3)) is

MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-Frequently Asked Questions
  1. Find the value of : sin^() (2 tan^(-1). 1/4) +cos (tan^(-1)2sqrt(2))

    Text Solution

    |

  2. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

    Text Solution

    |

  3. Show that sin^(-1)3/5-sin^(-1)8/(17)=cos^(-1)(84)/(85) .

    Text Solution

    |

  4. Prove that: sin^(-1)((5)/(13))+cos^(-1)((4)/(5))=(1)/(2)sin^(-1)((3696...

    Text Solution

    |

  5. Show that : 2 sin^(-1) (3/5)-tan^(-1) (17/31) = pi/4

    Text Solution

    |

  6. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

    Text Solution

    |

  7. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

    Text Solution

    |

  8. Prove that tan^(- 1)((6x-8x^3)/(1-12 x^2))-tan^(- 1)((4x)/(1-4x^2))=ta...

    Text Solution

    |

  9. Prove that tan ^(-1) . 1/5 + tan^(-1) . 1/7 + tan ^(-1) . 1/8 = pi/4

    Text Solution

    |

  10. Solve : 2 tan^(-1), (cos x) = tan^(-1), (2 cosec x)

    Text Solution

    |

  11. Solve : tan^(-1) 4x +tan^(-1)6x = pi/4

    Text Solution

    |

  12. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4,

    Text Solution

    |

  13. Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0...

    Text Solution

    |

  14. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

    Text Solution

    |

  15. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

    Text Solution

    |

  16. Express sin^(-1)((sin x+ cos x)/(2)), where -(pi)/(4) lt x lt (pi)/(4)...

    Text Solution

    |

  17. Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(...

    Text Solution

    |

  18. Simplify tan^(-1)[(acosx-bsinx)/(bcosx+asinx)], if a/btanx >-1 .

    Text Solution

    |

  19. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+)x+sqrt(1-x))]=pi/4...

    Text Solution

    |

  20. Prove the following: "cos"[tan^(-1){sin(cos t^(-1)x)}]= sqrt((1+x^2)/...

    Text Solution

    |