Home
Class 12
MATHS
Solve 2 cos^(-1) x + sin^(-1) x = (2pi)/...

Solve `2 cos^(-1) x + sin^(-1) x = (2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt3)/(2)`
`2 cos^(-1) x + sin^(-1) x = (2pi)/(3)`
`rArr cos^(-1) x (cos^(-1) x + sin^(-1) x) = (2pi)/(3)`
`rArr cos^(-1) x + (pi)/(2) = (2pi)/(3)`
`rArr cos^(-1) x = (pi)/(6) rArr x = (sqrt3)/(2)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

Similar Questions

Explore conceptually related problems

Solve : sin ^(-1) x+sin ^(-1) ""y=(2pi)/(3) and cos ^(-1) x- cos ^(-1)y =(pi)/(3).

sin ^(-1)cos sin^(-1)""x=(pi)/(3)

sin^(-1)x+sin ^(-1)""2x=(pi)/(3)

Solve 2 cos ^(2) x + 3 sin x =0

Solve 2 cos^(-1) x = sin^(-1) (2 x sqrt(1 - x^(2)))

Solve: sin^(-1) cos(sin^(-1)x) = pi/3 .

sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

Solve 2 cos^2 x + 3 sin x = 0

Solve : cos^(-1)x-sin^(-1)x=cos^(-1)(xsqrt(3))

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sin^-1x+sin^-1y=(2pi)/3, then cos^-1x+cos^-1y=

    Text Solution

    |

  2. solve the equation cot^-1 x + tan^-1 3 = pi/2

    Text Solution

    |

  3. Solve 2 cos^(-1) x + sin^(-1) x = (2pi)/(3)

    Text Solution

    |

  4. Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

    Text Solution

    |

  5. If sin^(-1)x+sin^(-1)y=(2pi)/3 and cos^(-1)x-cos^(-1)y=-pi/3 then the ...

    Text Solution

    |

  6. If (tan^-1x)^2+(cot^-1x)^2=(5pi^2)/8, then x equals

    Text Solution

    |

  7. Solve sec^(-1) x gt cosec^(-1) x

    Text Solution

    |

  8. Solve tan^(-1) x gt cot^(-1) x

    Text Solution

    |

  9. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

    Text Solution

    |

  10. If alpha in (-(pi)/(2), 0), then find the value of tan^(-1) (cot alpha...

    Text Solution

    |

  11. Find the maximum value of (sec^(-1) x) (cosec^(-1) x), x ge 1

    Text Solution

    |

  12. If equation sin^(-1) (4 sin^(2)theta + sin theta) + cos^(-1) (6 sin th...

    Text Solution

    |

  13. Find the value of sin^(-1) ((3)/(5)) + tan^(-1) ((1)/(7))

    Text Solution

    |

  14. If x gt y gt 0, then find the value of tan^(-1).(x)/(y) + tan^(-1) [(x...

    Text Solution

    |

  15. Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/...

    Text Solution

    |

  16. Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4

    Text Solution

    |

  17. The number of real values of x satisfying tan^-1(x/(1-x^2))+tan^-1 (1...

    Text Solution

    |

  18. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

    Text Solution

    |

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

    Text Solution

    |

  20. Solve the equation 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

    Text Solution

    |