Home
Class 11
MATHS
If f(x)="cos"^(2)x+"sec"^(2)x, then (i...

If `f(x)="cos"^(2)x+"sec"^(2)x`, then
(i) `f(x)lt1`
(ii) `f(x)=1`
(iii) `2ltf(x)lt1`
(iv) `f(x)ge2`

A

`f(x)lt1`

B

`f(x)=1`

C

`2ltf(x)lt1`

D

`f(x)ge2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINE

    ICSE|Exercise CHAPTER TEST |15 Videos

  • TRIGONOMETRIC EQUATIONS

    ICSE|Exercise CHAPTER TEST |6 Videos

Similar Questions

Explore conceptually related problems

If f(x)=cos^2x+s e c^2x ,t h e n f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

If f(x)=cos^2x+s e c^2x ,t h e n (a) f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

If f(x)=cos^2theta+sec^2theta, then f(x) f(x)>1 (d) f(x)geq2

If f(x)=x^(2) and g(x)=2x , then evaluate, (i) (f+g)(3)" "(ii) (f-g)(2) (iii) (f*g)(1)" "(iv) ((f)/(g))(5)

Let f(x)=(x^(2)-2x+1)/(x+3),f i n d x: (i) f(x) gt 0 (ii) f(x) lt 0

(d)/(dx) (AC)= f(x) (MC-AC) , then f(x)= (i) (1)/(x) (ii) x (iii) x^(-2) (iv) -x^(-1)

Find the intervals of monotonicity of the following functions. (i) f(x) =-x^(3) +6x^(2)-gx-2 (ii) f(x) =x+(1)/(x+1) (iii) f(x) =x. e^(x-x^(2)) (iv) f(x) =x- cosx

If f : R to R is defined as: f(x)={{:(2x+5","x gt 9),(x^(2)-1","-9 lt x lt 9),(x-4"," x lt -9):} then evaluate (i) f(2), (ii) f(10),(iii) f(-12) and (iv) f[f(3)] .

If f(x^(2) - 4x + 4) = x^(2) + 1 . Find f(1) if f(1) lt 8 .

Sketch the graph of {:((i) f(x)=sgn(x^(2)+1),(ii) f(x)=sgn(log_(e)x)),((iii) f(x)=sgn(sin x), (iv) f(x)=sgn(cos x)):}

ICSE-TRIGONOMETRIC FUNCTION-MULTIPLE CHOICE QUESTIONS
  1. The value of "cos"((3pi)/2+x)."cos"(2pi+x)["cot"((3pi)/(2)-x)+"cot"(2p...

    Text Solution

    |

  2. If sintheta+cosectheta=2, then "sin"^(2)theta+"cosec"^(2)theta is equa...

    Text Solution

    |

  3. If f(x)="cos"^(2)x+"sec"^(2)x, then (i) f(x)lt1 (ii) f(x)=1 (iii...

    Text Solution

    |

  4. If tantheta=1/(2) and tanphi=1/(3), then the value of (theta+phi) is

    Text Solution

    |

  5. Which of the following is not correct ?

    Text Solution

    |

  6. The value of "cos"1^(@)."cos"2^(@)."cos"3^(@)......."cos"179^(@) is

    Text Solution

    |

  7. The value of "tan"1^(@)."tan"2^(@)."tan"3^(@)......."tan"89^(@) is

    Text Solution

    |

  8. The value of "tan"75^(@)-"cot"75^(@) is equal to

    Text Solution

    |

  9. Which of the following is correct ?

    Text Solution

    |

  10. The value of "tan"5A-"tan"3A-"tan"2A is equal to

    Text Solution

    |

  11. The value of "sin"(45^(@)+ theta)-"cos(45^(@) - theta) is

    Text Solution

    |

  12. The value of "cot"(pi/(4)+theta)."cot"(pi/(4)-theta) is (i) -1 (ii...

    Text Solution

    |

  13. "cos"2theta."cos"2phi+"sin"^(2)(theta-phi)-"sin"^(2)(theta+phi) is equ...

    Text Solution

    |

  14. If for real x, "cos"theta=x+(1)/(x), then

    Text Solution

    |

  15. If "tan"A=1/(2),"tan"B=1/(3), then "tan"(2A+B) is equal to

    Text Solution

    |

  16. If alpha+beta=pi/(4), then (1+"tan"alpha)(1+"tan"beta) is

    Text Solution

    |

  17. If "sin"theta=-4/(5) and theta lies in third quadrant, then the value ...

    Text Solution

    |

  18. The greatest value of "sin"x."cos"x is

    Text Solution

    |

  19. acosx+bsinx lies between

    Text Solution

    |

  20. Number of solution of the equation tanx+secx=2cosx lying in the interv...

    Text Solution

    |