Home
Class 12
MATHS
Prove that: cos^(-1)(x)+cos^(-1)"{"x/2+...

Prove that: `cos^(-1)(x)+cos^(-1)"{"x/2+(sqrt(3-3x^2))/2")"=pi/3`

Text Solution

Verified by Experts

Let `cos^(-1)x=theta`. Then, `x=costheta` and `sqrt(1-x^(2))=sintheta`.
`therefore LHS=cos^(-1)x+cos^(-1)(x/2+sqrt(3)/2-sqrt(1-x^(2))`
`=theta+cos^(-1){cos(pi/3-theta)}=theta+(pi/3-theta)=pi/3` = RHS.
Hence, LHS=RHS.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4A|4 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4B|22 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

Find the value of cos^(-1)(x)+cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

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

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

Find the set of value of x for which the equation cos^(-1) x + cos^(-1) ((x)/(2) + (1)/(2) sqrt(3 -3x^(2))) = (pi)/(3) holds goods

If f(x)=cos^(-1)x+cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then

Prove that cos^(-1)((sqrt(1+x)+sqrt(1-x))/(2))=(pi)/(4)-(1)/(2)cos^(-1)x

If f(x) =cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))} then f(2/3) equals

cos^(-1)x sqrt(3)+cos^(-1)x=(pi)/(2)

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=sqrt(2)sin x

RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Objective Questons
  1. Prove that: cos^(-1)(x)+cos^(-1)"{"x/2+(sqrt(3-3x^2))/2")"=pi/3

    Text Solution

    |

  2. Find the principal value of: cos^(-1)((sqrt(3))/2)

    Text Solution

    |

  3. Find the principal value of the following: (i) cosec^(-1)(2) (ii) ta...

    Text Solution

    |

  4. Find the principal value of: cos^(-1)(-1/(sqrt(2)))

    Text Solution

    |

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

    Text Solution

    |

  6. The principal value of cos^(-1)(-1/2) is

    Text Solution

    |

  7. The principal value of tan^-1(-sqrt3) is

    Text Solution

    |

  8. The principal value of cot^(-1)(-1) is

    Text Solution

    |

  9. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

    Text Solution

    |

  10. The principal value of "cosec"^(-1)(-sqrt(2)) is

    Text Solution

    |

  11. Find the principal values of each of the following: cot^(-1)(-sqrt(...

    Text Solution

    |

  12. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

    Text Solution

    |

  13. The value of cos^(-1)(cos(14pi/6)) is

    Text Solution

    |

  14. The value of tan^(-1)(tan(8*pi/6)) is

    Text Solution

    |

  15. Find the value of : cot^(-1), (5pi/4)

    Text Solution

    |

  16. The value of sec^(-1)(sec(8pi)/5) is

    Text Solution

    |

  17. The value of "cosec"^(-1)("cosec"(4pi)/3) is

    Text Solution

    |

  18. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

    Text Solution

    |

  19. pi/3-sin^(-1)(-1/2)=?

    Text Solution

    |

  20. The value of sin(sin^(-1)(1/2)+cos^(-1)(1/2))=?

    Text Solution

    |

  21. If x ne 0 then cos(tan^(-1)+cot^(-1)x)=?

    Text Solution

    |