image

    Have a query? Ask a Tutor!!

    Access to best educators and exclusive paper discussions

    Offsite CampusTurito Championship

    Can’t find what you’re looking for?

    Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

    • Homework- One to One Solutions
    • Understand concepts to solve better
    • Get your doubts solved instantly
    Maths-
    General
    Easy

    Question

    if straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis where straight x element of straight R comma straight k greater or equal than 1 then straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals

    1. 1 over 6
    2. 1 third
    3. 1 over 9
    4. 1 over 12

    The correct answer is: 1 over 12

      Step by step solution:
      Given, f subscript k left parenthesis x right parenthesis space equals space 1 over kopen parentheses sin to the power of k x plus cos to the power of k x close parentheses
      Now, f subscript 4 left parenthesis x right parenthesis space minus space f subscript 6 left parenthesis x right parenthesis equals 1 fourth left parenthesis sin to the power of 4 x plus cos to the power of 4 x right parenthesisspace minus space 1 over 6 left parenthesis sin to the power of 6 x plus cos to the power of 6 x right parenthesis
      equals 1 fourth left parenthesis left parenthesis sin squared x plus cos squared x right parenthesis squarednegative 2 sin squared x space cos squared x right parenthesisnegative 1 over 6 left parenthesis left parenthesis sin squared x plus cos squared x right parenthesis cubed minus3 space sin squared x space cos squared x left parenthesissin squared x plus cos squared x right parenthesis right parenthesis
      equals 1 fourth left parenthesis 1 minus 2 sin squared x space cos squared x right parenthesisnegative 1 over 6 left parenthesis 1 minus 3 sin squared x cos squared x right parenthesis                [ since sin squared theta plus cos squared theta equals 1 ]
      equals 1 fourth minus 1 half sin squared x cos squared xnegative 1 over 6 plus 1 half sin squared x cos squared x
      equals 1 fourth minus 1 over 6equals 1 over 12
      Hence, option(b) is the correct option.

      Related Questions to study

      General
      Maths-

      Two arcs of same length of two different circles subtended angles of  25 to the power of ring operator and 75 to the power of ring operator  at their centers respectively. Then the ratio of the radii of the circles is

      Two arcs of same length of two different circles subtended angles of  25 to the power of ring operator and 75 to the power of ring operator  at their centers respectively. Then the ratio of the radii of the circles is

      Maths-General
      General
      Maths-

      Let theta element of left parenthesis 0 comma pi divided by 4 right parenthesis and straight t subscript 1 equals left parenthesis tan space theta right parenthesis to the power of me theta end exponent comma straight t subscript 2 equals left parenthesis tan space theta right parenthesis to the power of cot space theta end exponent comma straight t subscript 3 equals left parenthesis cot space theta right parenthesis to the power of con space theta end exponent straight t subscript 4 equals left parenthesis cot space theta right parenthesis to the power of cos space theta end exponent then

      Let theta element of left parenthesis 0 comma pi divided by 4 right parenthesis and straight t subscript 1 equals left parenthesis tan space theta right parenthesis to the power of me theta end exponent comma straight t subscript 2 equals left parenthesis tan space theta right parenthesis to the power of cot space theta end exponent comma straight t subscript 3 equals left parenthesis cot space theta right parenthesis to the power of con space theta end exponent straight t subscript 4 equals left parenthesis cot space theta right parenthesis to the power of cos space theta end exponent then

      Maths-General
      General
      Maths-

      straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow

      straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow

      Maths-General
      parallel
      General
      Maths-

      Ix equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow

      Ix equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow

      Maths-General
      General
      Maths-

      If ABCD is a cynic quadrilateral such that 12 tan A minus 5 equals 0 and 5cos B+3=0, then cos C tan D=

      If ABCD is a cynic quadrilateral such that 12 tan A minus 5 equals 0 and 5cos B+3=0, then cos C tan D=

      Maths-General
      General
      Maths-

      integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction = A log |x + 1| + C for x < – 1 then A is -

      integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction = A log |x + 1| + C for x < – 1 then A is -

      Maths-General
      parallel
      General
      Maths-

      cos space A comma sin space A comma cot space A spaceare in then tan to the power of 6 straight A minus tan squared space of 1em straight A equals

      cos space A comma sin space A comma cot space A spaceare in then tan to the power of 6 straight A minus tan squared space of 1em straight A equals

      Maths-General
      General
      Maths-

      straight f left parenthesis straight x right parenthesis equals straight x cubed minus 2 straight x squared plus 3 straight x minus 5 not stretchy rightwards double arrow straight f open square brackets sin space open parentheses fraction numerator 5 straight pi over denominator 2 end fraction close parentheses close square brackets plus straight f open square brackets sin space open parentheses fraction numerator 3 straight pi over denominator 2 end fraction close parentheses close square brackets equals

      straight f left parenthesis straight x right parenthesis equals straight x cubed minus 2 straight x squared plus 3 straight x minus 5 not stretchy rightwards double arrow straight f open square brackets sin space open parentheses fraction numerator 5 straight pi over denominator 2 end fraction close parentheses close square brackets plus straight f open square brackets sin space open parentheses fraction numerator 3 straight pi over denominator 2 end fraction close parentheses close square brackets equals

      Maths-General
      General
      Maths-

      If cos theta equals 3 over 5 and theta is not in the first quadrant, then fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals

      If cos theta equals 3 over 5 and theta is not in the first quadrant, then fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals

      Maths-General
      parallel
      General
      Maths-

      text  If  end text a sin space theta plus b cos comma theta equals c text  then  end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals

      text  If  end text a sin space theta plus b cos comma theta equals c text  then  end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals

      Maths-General
      General
      Maths-

      cosec squared space alpha equals fraction numerator 4 x y over denominator left parenthesis x plus y right parenthesis squared end fraction left square bracket left parenthesis x comma y right parenthesis not equal to left parenthesis 0 comma 0 right parenthesis right square bracket text  is  end text

      cosec squared space alpha equals fraction numerator 4 x y over denominator left parenthesis x plus y right parenthesis squared end fraction left square bracket left parenthesis x comma y right parenthesis not equal to left parenthesis 0 comma 0 right parenthesis right square bracket text  is  end text

      Maths-General
      General
      Maths-

      text  If  end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text  then  end text x equals

      text  If  end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text  then  end text x equals

      Maths-General
      parallel
      General
      Maths-

      if sin space theta plus cos space theta equals p and sin cubed space theta plus cos cubed space theta equals q then straight p open parentheses straight p squared minus 3 close parentheses equals

      if sin space theta plus cos space theta equals p and sin cubed space theta plus cos cubed space theta equals q then straight p open parentheses straight p squared minus 3 close parentheses equals

      Maths-General
      General
      Chemistry-

      In the reaction

      the structure of the product Tis:

      In the reaction

      the structure of the product Tis:

      Chemistry-General
      General
      Chemistry-

      In the reaction for denigration,

      the major dinitrated product (X) is:

      In the reaction for denigration,

      the major dinitrated product (X) is:

      Chemistry-General
      parallel

      card img

      With Turito Academy.

      card img

      With Turito Foundation.

      card img

      Get an Expert Advice From Turito.

      Turito Academy

      card img

      With Turito Academy.

      Test Prep

      card img

      With Turito Foundation.