Home
Class 12
MATHS
If (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5 pi...

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

Text Solution

Verified by Experts

The given equation can be written as :
`(tan^(−1)x+cot^(−1)x)^2−2tan^(−1)x(π/2​−tan^(−1)x)=(5π^2)/8​`
`2(tan^(−1)x)^2−2(π/2​)tan^(−1)(x)−(3π^2)/8​=0`
`tan^(−1)x=−π/4​` or `(3π)/4`​
Hence, `tan^(−1)x=1`
...
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 (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5 pi^(2))/(8) find x

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

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

If (sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5 pi^(2))/(8) then one of the values of x is

Solve for x: (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5*pi^(2))/(8)

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Write the value of 2sin^(-1)\ 1/2+cos^(-1)((a-b)/(a+b))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1...

    Text Solution

    |

  19. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

    Text Solution

    |

  20. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

    Text Solution

    |