Home
Class 12
MATHS
If sin^(-1)x=pi/5, for some x in (-1,1),...

If `sin^(-1)x=pi/5`, for some `x in (-1,1),` then find the value of `cos^(-1)x`

Text Solution

Verified by Experts

`sin^(-1) x + cos^(-1) x = (pi)/(2) " or " cos^(-1) x = (pi)/(2) - sin^(-1) x = (pi)/(2) - (pi)/(5) = (3pi)/(10)`
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

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

If tan(cos^(-1) x) = sin (cot^(-1)(1/2)) , then find the value of x

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)(1/x)+cos^(-1)(1/y)

If cos(2sin^(-1)x)=1/9, then find the values of xdot

If sin(sin^(-1)(1/5)+cos^(-1)x)=1 , then find the value of x.

If cos^(-1)((6x)/(1+9x^2))=-pi/2+2tan^(-1)3x , then find the value of x

y=sin^(-1)(x/2)+cos^(-1)(x/2) then find the value of [dy/dx]_(x=1)

Find the values of each of the following : If sin ("sin"^(-1)1/5+"cos"^(-1)x)=1 then find the value of x.

If sin^(-1)x_i in [0,1]AAi=1,2,3, .28 then find the maximum value of sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+ sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)++sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to cot^...

    Text Solution

    |

  2. Prove that costan^(-1)sincot^(-1)x=sqrt((x^2+1)/(x^2+2))

    Text Solution

    |

  3. If sin^(-1)x=pi/5, for some x in (-1,1), then find the value of cos^(-...

    Text Solution

    |

  4. If sin(sin^(-1)(1/5)+cos^(-1)x)=1, then find the value of x.

    Text Solution

    |

  5. Solve sin^(-1)xlt=cos^(-1)xdot

    Text Solution

    |

  6. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

    Text Solution

    |

  7. Find the minimum value of (sec^(-1)x)^2+("c o s e c"^(-1))^2

    Text Solution

    |

  8. Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

    Text Solution

    |

  9. Solve sin^(-1)((14)/(|x|))+sin^(-1)((2sqrt(15))/(|x|))=pi/2

    Text Solution

    |

  10. If alpha=sin^(-1)(cos(sin^(-1)x))a n dbeta=cos^(-1)("sin"(cos^(-1)x)),...

    Text Solution

    |

  11. Is sec^(-1)x= cosec^(-1)y, then the value of cos^(-1)(1/x)+cos^(-1)(1/...

    Text Solution

    |

  12. Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//...

    Text Solution

    |

  13. Find the value of sin^(-1)x+sin^(-1)(1/x)+cos^(-1)x+cos^(-1)(1/x)dot

    Text Solution

    |

  14. Find the value of sum(r=1)^(10)sum(s=1)^(10)tan^(-1)(r/s)dot

    Text Solution

    |

  15. If sin^(-1)xi in [0,1]AAi=1,2,3, .28 then find the maximum value of s...

    Text Solution

    |

  16. If two angles of a triangle are tan^(-1) (2) and tan^(-1) (3), then fi...

    Text Solution

    |

  17. Prove that cos^(-1).(4)/(5) + cos^(-1).(12)/(13) = cos^(-1).(33)/(65)

    Text Solution

    |

  18. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A) =0

    Text Solution

    |

  19. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

    Text Solution

    |

  20. Simplify tan^(-1) [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [...

    Text Solution

    |