Home
Class 12
MATHS
If sin^(-1)(1/3)+cos^(-1)x=pi/2,then fin...

If `sin^(-1)(1/3)+cos^(-1)x=pi/2`,then find `x`

Text Solution

Verified by Experts

`sin^(−1)(1/3)​+cos^(−1)x=π/2​`
`⇒cos^(−1)x=π/2​−sin^(−1)(1/3)​`
`⇒x=cos(π/2​−sin^(−1)(1/3)​)`
`⇒x=sin(sin^(−1)(1/3)​)`
`∴x=1/3`​
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 sin^(-1)(5/x)+cos^(-1)(x/5)=pi/2 ,then find x.

If sin^(-1)x+2cos^(-1)x=(2pi)/3 , then find x.

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then x in

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then x in

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

sin^(-1)((x)/(2))+cos^(-1)(x)=(Pi)/(6), then find x

If sin^(-1)(e^(x))+cos^(-1)(x^(2))=(pi)/(2), then find the number of solutions of this equation

If sin^(-1)x=(pi)/(3) then find cos^(-1)x

If sin^(-1) x + sin^(-1) y = (2pi)/3", then " cos^(-1) x + cos^(-1) y

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Write the principal value of cos^(-1)(cos(2pi)/3)+sin^(-1)(s in(2pi)/3...

    Text Solution

    |

  2. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2,t h e nfin dxdot

    Text Solution

    |

  3. If sin^(-1)(1/3)+cos^(-1)x=pi/2,then find x

    Text Solution

    |

  4. Write the value of 2sin^(-1)\ 1/2+cos^(-1)((a-b)/(a+b))

    Text Solution

    |

  5. Evaluate: sin^(-1)(s in(3pi)/5)

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

    Text Solution

    |

  8. Evaluate: (i) tan{cos^(-1)(-7/(25))} (ii) "c o s e c"{cot^(-1)(-(12)/...

    Text Solution

    |

  9. Evaluate: sin{cos^(-1)(-(3)/5)+cot^(-1)(-5/(12))}

    Text Solution

    |

  10. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=(2pi)/3, find the valu...

    Text Solution

    |

  11. If tan^(-1)x+tan^(-1)y=(4pi)/5, find cot^(-1)x+cot^(-1)ydot

    Text Solution

    |

  12. If tan^(-1)x-cot^(-1)x=tan^(-1)""1/(sqrt(3)) find the value of xdot

    Text Solution

    |

  13. If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find the value of xdot

    Text Solution

    |

  14. If cos(sin^(-1)(2/5)+cos^(-1)x)=0 find the value of xdot

    Text Solution

    |

  15. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

    Text Solution

    |

  16. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

    Text Solution

    |

  17. If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/...

    Text Solution

    |

  18. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

    Text Solution

    |

  19. If alpha=tan^(-1)(t a n(5pi)/4)a n dbeta=tan^(-1)(-tan(2pi)/3),t h e n...

    Text Solution

    |

  20. The domain of cos^(-1)(x^2-4) is (a) [3,5] (b) [-1,1] (c)[-sqrt(5),-...

    Text Solution

    |