Maths-
General
Easy

Question

cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals

  1. 1
  2. 3
  3. negative square root of 3
  4. square root of 3

hintHint:

In this question, we have to find the value of m in cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets. For this first we will simplify the given trigonometric function then assume the range of the function to find the range of the given function. Then we will compare the range derived o the range given to find the required value of m.

The correct answer is: square root of 3


    space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses
equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets
equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses
equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses
equals negative square root of 3. cos space x. sin space x
equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x equals 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction
F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction
A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets
S o comma space m equals square root of 3

    Related Questions to study

    General
    Maths-

    cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of

    cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of

    Maths-General
    General
    physics-

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    physics-General
    General
    physics-

    The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

    The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

    physics-General
    parallel
    General
    physics-

    For the circuit shown in figure the charge on 4muF capacitor is

    For the circuit shown in figure the charge on 4muF capacitor is

    physics-General
    General
    Maths-

    The minimum and maximum values of sin to the power of 4 x plus cos to the power of 4 space x are

    The minimum and maximum values of sin to the power of 4 x plus cos to the power of 4 space x are

    Maths-General
    General
    physics-

    Figure shows a network of eight resistors, each equal to 2blank capital omega, connected to a 3V battery of negligible internal resistance. The current I in the circuit is

    Figure shows a network of eight resistors, each equal to 2blank capital omega, connected to a 3V battery of negligible internal resistance. The current I in the circuit is

    physics-General
    parallel
    General
    physics-

    The equivalent resistance between A blank a n d blank B in the given circuit is

    The equivalent resistance between A blank a n d blank B in the given circuit is

    physics-General
    General
    chemistry-

    Which of the following is/are the rate determining step(s) of the given reaction?

    Which of the following is/are the rate determining step(s) of the given reaction?

    chemistry-General
    General
    Maths-

    Maximum value of  fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction

    Maximum value of  fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction

    Maths-General
    parallel
    General
    Maths-

    The minimum and maximum values of 2 square root of 2 cos space x plus sin space x are

    The minimum and maximum values of 2 square root of 2 cos space x plus sin space x are

    Maths-General
    General
    chemistry-


    (A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?


    (A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?

    chemistry-General
    General
    chemistry-

    Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

    Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

    chemistry-General
    parallel
    General
    Maths-

    16 sin x cos space x cos space 2 x cos space 4 x cos space 8 x element of

    16 sin x cos space x cos space 2 x cos space 4 x cos space 8 x element of

    Maths-General
    General
    physics-

    Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

    Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

    physics-General
    General
    physics-

    The figure shows a network of currents. The magnitude of current is shown here. The current I will be

    The figure shows a network of currents. The magnitude of current is shown here. The current I will be

    physics-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.