Home
Class 12
MATHS
If y =4sin^(2)theta-cos2theta,then y lie...

If `y =4sin^(2)theta-cos2theta`,then `y` lies in the interval

A

`(-1,5)`

B

`[-1,5]`

C

`(-oo,-1)uu(5,oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `x=4sin^(2)theta-cos2 theta.Then,`
`x=2(1-cos2theta)-cos2 theta`
`impliesx=2-3cos2 theta`
Now, `-3le-3cos2 thetale3" "[because-1le cos 2 thetale1]`
`implies2-3le2-3cos2 thetale2+3`
`implies-1lex le5impliesx in[-1,5].`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Exercise|190 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If y=4sin^(2)theta-cos2 theta, then y lies in the interval

If A-2sin^(2)theta-cos2 theta, then A lies in the interval [-1,3](1,2](c)[-2,4](d) none of these

For -pi/2 lt theta lt pi/2, (sintheta + sin 2theta)/(1+costheta + cos2theta) lies in the interval

For -pi/2

For -(pi)/(2)

For -(pi)/(2)lttheta(pi)/(2),(sintheta+sin2theta)/(1+costheta+cos2theta) lies in the interval

The solution of the equation cos^(2)theta+sin theta+1=0 lies in the interval

OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. In a DeltaABC, if tanA+2tanB=0, then which one is correct?

    Text Solution

    |

  2. The maximum value of 1+sin(pi/4+theta)+2cos(pi/4-theta) for real value...

    Text Solution

    |

  3. If y =4sin^(2)theta-cos2theta,then y lies in the interval

    Text Solution

    |

  4. If y=cos^2theta+sin^4theta then for all real values of theta

    Text Solution

    |

  5. The ratio of the greatest value of 2-cos x+s in^2x to its least value ...

    Text Solution

    |

  6. The least value of [cos^2 theta-6 sin theta. cos theta+3 sin^2 theta +...

    Text Solution

    |

  7. If y=tan^(2)theta+sectheta, thetane(2n+1)pi//2,then

    Text Solution

    |

  8. Two parallel chords of a circle, which are on the same side of centre,...

    Text Solution

    |

  9. If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then

    Text Solution

    |

  10. If sinx+cosx=1/5,0lexlepi, then tan x is equal to

    Text Solution

    |

  11. For for A=133^(@),2cos""A/2is equal to

    Text Solution

    |

  12. A and B are positive acute angles satisfying the equations 3cos^(2)A+2...

    Text Solution

    |

  13. The expression (cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx) is equ...

    Text Solution

    |

  14. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

    Text Solution

    |

  15. The expression 2^(sintheta)+2^(-costheta) is minimum when theta is equ...

    Text Solution

    |

  16. If A is an obtause angle, then (sin^(3)A-cos^(3)A)/(sinA-cosA)+(sinA)/...

    Text Solution

    |

  17. In a triangle ABC, cos 3A + cos 3B + cos 3C = 1, then find any one ang...

    Text Solution

    |

  18. If alpha,beta,gamma,delta are the smallest positive angles in ascendin...

    Text Solution

    |

  19. If 0 ltx lt pi/2 and sin^n x + cos^n x gt= 1, then

    Text Solution

    |

  20. In a DeltaABC, cos A+cos B+cosC belongs to the interval

    Text Solution

    |