Home
Class 12
MATHS
Prove that 3 sin ^(-1) x = sin^(-1) (3x ...

Prove that `3 sin ^(-1) x = sin^(-1) (3x - 4x^3),
x in [-1/2,1/2]`

Text Solution

Verified by Experts

Put `sin^(-1) x = y`. Then sin y = x
`therefore 3 x - 4 x^3 = 3 sin y - 4 sin^3 y = sin 3y`
`implies 3y = sin^(-1) (3x - 4x^3)`
`implies 3 sin^(-1) x = sin^(-1) (3x - 4x^3)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|22 Videos

  • INTEGRALS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|291 Videos

  • LINEAR PROGRAMMING

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|40 Videos

Similar Questions

Explore conceptually related problems

prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]

Prove that sin^-1(2xsqrt(1-x^2))=2sin^-1x

Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

Prove that cos^-1x=2sin^-1sqrt((1-x)/2)

Prove that cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)

sin^(-1)(1-x)-2sin^(-1)x= pi/2 ,then find x

Prove that (sin 5 x+sin 3 x)/(cos 5 x+cos 3 x)=tan 4 x

Prove that (sin 3 x+sin x) sin x+(cos 3 x-cos x)cosx=0

Prove that tan ^(-1) x+tan ^(-1) ((2 x)/(1-x^2))=tan ^(-1)((3 x-x^3)/(1-3 x^2)),|x|lt1/sqrt3

Prove that (sin5x+sin3x)/(cos5x+cos3x) = tan 4x

A N EXCEL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. prove that tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]

    Text Solution

    |

  2. Prove that 3 sin ^(-1) x = sin^(-1) (3x - 4x^3), x in [-1/2,1/2]

    Text Solution

    |

  3. prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]

    Text Solution

    |

  4. Prove that tan^(-1)(2/11) + tan^(-1)(7/24) = tan^(-1)(1/2)

    Text Solution

    |

  5. Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

    Text Solution

    |

  6. Write the following functions in the simplest form : tan^(-1)((sqrt(...

    Text Solution

    |

  7. Write the following functions in the simplest form : tan^(-1)(1/sqrt...

    Text Solution

    |

  8. Write the following functions in the simplest form : tan^(-1) sqrt((...

    Text Solution

    |

  9. Write the following functions in the simplest form : tan^(-1)((cos x...

    Text Solution

    |

  10. Write the following functions in the simplest form : tan^(-1) (x/sqr...

    Text Solution

    |

  11. Write the following functions in the simplest form : tan^(-1)((3a^2x...

    Text Solution

    |

  12. Find the value of tan^(-1)[2 cos(2sin^(-1)frac(1)(2) )]

    Text Solution

    |

  13. Find the value of cot(tan^(-1) a + cot^(-1) a)

    Text Solution

    |

  14. Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x...

    Text Solution

    |

  15. If sin(sin^-1(frac(1)(5))+cos^-1(x))=1

    Text Solution

    |

  16. If tan^(-1) ((x-1)/(x-2)) + tan^(-1) ((x+1)/(x+2)) = pi/4. then find t...

    Text Solution

    |

  17. Find the value of sin^(-1)sin((2pi)/3)

    Text Solution

    |

  18. Find the values of the following : tan^(-1)(tan frac (3pi)4)

    Text Solution

    |

  19. Evaluate tan(sin^-1frac(3)(5)+cot^-1frac(3)(2))

    Text Solution

    |

  20. find the value of cos^-1cos((7pi)/3)

    Text Solution

    |