Home
Class 11
MATHS
The equation tan^4x-2sec^2x+a=0 will ha...

The equation `tan^4x-2sec^2x+a=0` will have at least one solution if

Text Solution

Verified by Experts

`tan^4x-2sec^2x +a = 0`
`=>tan^4x-2(1+tan^2x) +a = 0`
`=>tan^4x-2tan^2x -2 +a = 0`
`=>tan^4x-2tan^2x +1-3 +a = 0`
`=>(tan^2x - 1)^2 = 3-a`
To have at least one solution for this equation,
`3-a ge 0`
`=>a le 3`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

The equation tan^(4)x-2sec^(2)x+a^(2)=0 will have at least one solution, if

If the equation cot^(4)x-2cos ec^(2)x+a^(2)=0 has at least one solution,then the sum of all possible integral values of a is equal to a.4b .3c.2d.0

The interval of a for which the equation tan^(2)x-(a-4)tan x+4-2a=0 has at least one solution AA x in[0,pi/4]a in(2,3) b.a in[2,3] c.a in(1,4) d.a in[1,4]

If the equation x^(2)+4+3sin(ax+b)-2x=0 has at least one real solution, where a,b in [0,2pi] then one possible value of (a+b) can be equal to

The equation cos^(4)x-sin^(4)x+cos2x+alpha^(2)+alpha=0 will have at least one solution, if

The equation 3tan^(4)x-10tan^(2)x+3=0 has the solution set as

The equation 3tan^(4)x-10tan^(2)x+3=0 has the solution set as

If a,b in(0,2) and the equation (2x^(2)+5)/(2)=x-2cos(ax+b) has at least one solution then

The total number of solutions of the equation tan x+sec x=2 which lie in the interval [0,2 pi] is

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Three parallel chords of a circle have lengths 2,3,4 units and subtend...

    Text Solution

    |

  2. Prove that cos36^0cos72^0cos108^0cos144^0=1/(16)dot

    Text Solution

    |

  3. The equation tan^4x-2sec^2x+a=0 will have at least one solution if

    Text Solution

    |

  4. A tower P Q stands at a point P within the triangular park A B C such ...

    Text Solution

    |

  5. The total number of ordered pairs (x , y) satisfying |x|+|y|=2,sin((p...

    Text Solution

    |

  6. If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin...

    Text Solution

    |

  7. Prove that a(bcosC-ccosB)=b^2-c^2

    Text Solution

    |

  8. If 4sin^4x+cos^4x=1,then x is equal to (n in Z) (a)npi (b) npi+-...

    Text Solution

    |

  9. If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/...

    Text Solution

    |

  10. If in a triangle a cos^2C/2+ c cos^2A/2=(3b)/2, then find the relatio...

    Text Solution

    |

  11. Evaluate cosacos2acos3a cos 999 a , where a=(2pi)/(1999)dot

    Text Solution

    |

  12. If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z)...

    Text Solution

    |

  13. Find the number of pairs of integer (x , y) that satisfy the followin...

    Text Solution

    |

  14. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

    Text Solution

    |

  15. Let A D be a median of the A B Cdot If A Ea n dA F are medians of ...

    Text Solution

    |

  16. Find the value of cos12^0+cos84^0+cos156^0+cos132^0

    Text Solution

    |

  17. If no solution of 3siny+12sin^3x=a lies on the line y=3x , then a in ...

    Text Solution

    |

  18. Find the angle theta whose cosine is equal to its tangent.

    Text Solution

    |

  19. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |

  20. If in triangle the angles are in the ratio as 1:2:3 , prove that the ...

    Text Solution

    |