Home
Class 12
MATHS
If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)...

If `alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)),beta=2sin^(-1)((2x)/(1+x^2))` and `tanpi/8=k ,` then (a) `alpha+beta=pi` for `x in [1,1/k]` (b)`alpha+beta` for `x in (-k , k)` (c) `alpha+beta=pi` for`x in [1,1/k]` (d) `alpha+beta=0` for `x in [-k , k]`

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

underset(x rarr 0)lim (sin alpha x)/(e^(beta x) - 1) (alpha, beta != 0) equal to -

If cos alpha = k cos beta , "show that", "tan" ( alpha+beta)/2 = ( 1-k)/(1+k)"cot" (alpha-beta)/2

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" "tan" (alpha + beta)/2=

Prove that 2tan^(-1)[tan((alpha)/(2)) tan((pi)/(4)-(beta)/(2))]=tan^(-1)((sin alpha cos beta)/(cos alpha+sin beta))

If cos alpha = k cos beta Show that tan ((alpha+beta)/2)=(1-k)/(1+k)cot((alpha-beta)/2)

If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

If tan alpha = (x sin beta)/(1-x cos beta) " and " tan beta = (y sin alpha)/(1-y cos alpha),"show that", (sin alpha)/(sin beta) = x/y .

Let , alpha, beta in RR be such that underset(x rarr 0)lim (x^(2) sin (beta x))/(alpha x - sin x) = 1 . Then 6(alpha + beta) equals

x(x-3)=4,has two roots alpha and beta then alpha^2+beta^2=?

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

    Text Solution

    |

  2. If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x ...

    Text Solution

    |

  3. If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)),beta=2sin^(-1)((2x)/(1+x^2))...

    Text Solution

    |

  4. Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sq...

    Text Solution

    |

  5. Solve the equation tan^(-1)2x+tan^(-1)3x=pi/4

    Text Solution

    |

  6. Solve tan^(-1)x+sin^(-1)x=tan^(-1)2xdot

    Text Solution

    |

  7. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),where x in R-{-1,1}, is equal to

    Text Solution

    |

  8. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

    Text Solution

    |

  9. Prove that: tan^(-1)x+tan^(-1)(1/x)={pi/2,ifx >0-pi/2,ifx<0

    Text Solution

    |

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

    Text Solution

    |

  11. Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If two angles of a triangle are tan^(-1)(2)a n dtan^(-1)(3), then find...

    Text Solution

    |

  15. Find the sum of the following AP : 0.6, 1.7, 2.8, ……, to 100 terms.

    Text Solution

    |

  16. Find the sum of the following AP -37, -33, -29, …… to 12 terms.

    Text Solution

    |

  17. Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/...

    Text Solution

    |

  18. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  19. sum(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1))))is equal to (a...

    Text Solution

    |

  20. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

    Text Solution

    |