Home
Class 12
MATHS
Prove that: sin{tan^(-1)((1-x^2)/(2x))...

Prove that: `sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1`

Text Solution

Verified by Experts

`sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1`
Let `x = tan theta`
`sin [tan^(-1) [1 – x^2] / (2x) + cos^(-1) [1 – x^2] / [1 + x^2]`
`= sin [tan^(-1) (cot 2theta) + cos^(-1) cos 2theta]`
`= sin [tan^(-1) tan ((pi) / 2 – 2theta) + 2theta]` ...
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

If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

Prove that 2tan^(-1)((1+x)/(1-x))+sin^(-1)((1-x^(2))/(1+x^(2)))=pi

tan ^ (-1) ((1-x ^ (2)) / (2x)) + sin ^ (-1) ((2x) / (1 + x ^ (2))) =

Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

prove that tan^(-1)(sqrt(x))=(1)/(2)cos^(-1)((1-x)/(1+x)),x in[0,1]

simplify 2tan^(-1)((1+x)/(1-x))+sin^(-1)((1-x^(2))/(1+x^(2)))

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is

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

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

    Text Solution

    |

  2. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

    Text Solution

    |

  3. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

    Text Solution

    |

  4. Find the principal values of (a) sin^(-1)((sqrt(3))/2) (b) sin^(-1)(...

    Text Solution

    |

  5. Find the principal values of sin^(-1)(1/2)

    Text Solution

    |

  6. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}] .

    Text Solution

    |

  7. Find the domain of the function f(x)=sin^(-1)(2x-3) .

    Text Solution

    |

  8. Find the domain of f(x)=sin^(-1)(-x^2)dot

    Text Solution

    |

  9. Find the domain of f(x)=sin^(-1)x+cosx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Let x ,\ y ,\ z in [-1,\ 1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=(3...

    Text Solution

    |

  13. Let x ,\ y ,\ z in [-1,\ 1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=(3...

    Text Solution

    |

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

    Text Solution

    |

  15. Find the principal value of each of the following: (i) sin^(-1)((sq...

    Text Solution

    |

  16. If tan^(-1)x = y then

    Text Solution

    |

  17. Find the value of sin^(-1){cos(sin^(-1)(sqrt(3)/2))}

    Text Solution

    |

  18. Find the domain of each of the following functions: (i) f(x)=sin^(-...

    Text Solution

    |

  19. Find the domain of each of the following functions: (i) f(x)=sin^(-...

    Text Solution

    |

  20. If sin^(-1)x+sin^(-1)y+sin^(-1)z+sin^(-1)t=2pi , then find the value ...

    Text Solution

    |