Maths-
General
Easy

Question

If a,b,c are in A.P the cot space A over 2 comma cot space B over 2 comma cot space C over 2 are in

  1. A.P
  2. G.P
  3. H.P
  4. A.G.P

hintHint:

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

The correct answer is: A.P



    bold italic W bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold comma bold space bold 2 bold italic s bold equals bold italic a bold plus bold italic b bold plus bold space bold italic c
bold italic A bold italic n bold italic d bold space bold italic A bold italic l bold italic s bold italic o bold space bold italic w bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold space bold semicolon bold space bold italic c bold italic o bold italic t bold space bold A over bold 2 bold space bold equals bold space fraction numerator bold s bold left parenthesis bold s bold minus bold a bold right parenthesis over denominator bold capital delta end fraction
a comma space b comma space c space i n space A. P. space space space space space space space space space space space space space space space space space space
bold italic o bold italic r bold comma space left parenthesis s minus a right parenthesis comma space left parenthesis s minus b right parenthesis comma space left parenthesis s minus c right parenthesis space i n space A. P.
bold italic o bold italic r bold comma space s left parenthesis s minus a right parenthesis comma space s left parenthesis s minus b right parenthesis comma space s left parenthesis s minus c right parenthesis space i n space A. P.
bold italic o bold italic r bold comma fraction numerator space s left parenthesis s minus a right parenthesis over denominator straight capital delta end fraction comma space fraction numerator space s left parenthesis s minus b right parenthesis over denominator straight capital delta end fraction comma space fraction numerator space s left parenthesis s minus c right parenthesis over denominator straight capital delta end fraction space i n space A. P.
T h e r e f o r e comma
bold italic c bold italic o bold italic t bold space bold A over bold 2 bold comma bold space bold italic c bold italic o bold italic t bold space bold B over bold 2 bold comma bold space bold italic c bold italic o bold italic t bold space bold C over bold 2 bold space bold italic a bold italic l bold italic s bold italic o bold space bold italic i bold italic n bold space bold italic A bold. bold italic P bold.
    img

    If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.

    Related Questions to study

    General
    biology

    Systemic heart refers to

    Systemic heart refers to

    biologyGeneral
    General
    biology

    Which is a analgesic drug

    Which is a analgesic drug

    biologyGeneral
    General
    biology

    Penicillin was discovered by -

    Penicillin was discovered by -

    biologyGeneral
    parallel
    General
    Maths-

    If fraction numerator b over denominator c plus a end fraction plus fraction numerator c over denominator a plus b end fraction equals 1 then

    All three sides are equal. All three angles are congruent and are equal to 60 degrees. It is a regular polygon with three sides. The perpendicular drawn from vertex of the equilateral triangle to the opposite side bisects it into equal halves.

    If fraction numerator b over denominator c plus a end fraction plus fraction numerator c over denominator a plus b end fraction equals 1 then

    Maths-General

    All three sides are equal. All three angles are congruent and are equal to 60 degrees. It is a regular polygon with three sides. The perpendicular drawn from vertex of the equilateral triangle to the opposite side bisects it into equal halves.

    General
    physics-

    Two bodies of mass 1 kg and 3 kg have position vector left parenthesis straight i plus 2 straight j with not stretchy hat on top plus straight k right parenthesis times text  and  end text times left parenthesis negative 3 straight i minus 2 straight j plus straight k right parenthesis   respectively the center of mass of this system has a position vector.

    Two bodies of mass 1 kg and 3 kg have position vector left parenthesis straight i plus 2 straight j with not stretchy hat on top plus straight k right parenthesis times text  and  end text times left parenthesis negative 3 straight i minus 2 straight j plus straight k right parenthesis   respectively the center of mass of this system has a position vector.

    physics-General
    General
    Maths-

    In straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan A over 2 plus tan space B over 2 close parentheses equals

    In straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan A over 2 plus tan space B over 2 close parentheses equals

    Maths-General
    parallel
    General
    physics-

    In HCl macule the separation between the nuclei of the two atoms is about1.27 straight A open parentheses IA equals 10 to the power of negative 10 end exponent straight m close parentheses The approximate location of the center of mass of the molecule is - -A,i with respect of Hydrogen atom ( mass of  is 35.5 times of mass of Hydrogen)

    In HCl macule the separation between the nuclei of the two atoms is about1.27 straight A open parentheses IA equals 10 to the power of negative 10 end exponent straight m close parentheses The approximate location of the center of mass of the molecule is - -A,i with respect of Hydrogen atom ( mass of  is 35.5 times of mass of Hydrogen)

    physics-General
    General
    chemistry-

    Concrete is produced from a mixture of cement, water and small stones. Small amount of gypsum, C a S O subscript 4 times 2 H subscript 2 O is added in cement production to improve the subsequent hardening of concrete. The elevated temperature during the production of cement may lead to the formation of unwanted hemihydrate
    C a S O subscript 4 times 1 half H subscript 2 O according to reaction,
    C a S O subscript 4 times 2 H subscript 2 O open parentheses s close parentheses rightwards arrow C a S O subscript 4 times 1 half H subscript 2 O open parentheses s close parentheses plus 3 over 2 H subscript 2 O left parenthesis g right parenthesis
    The increment subscript f end subscript H to the power of ⊖ end exponentofC a S O subscript 4 times 2 H subscript 2 O open parentheses s close parentheses comma blank C a S O subscript 4 times 1 half H subscript 2 O open parentheses s close parentheses comma H subscript 2 O left parenthesis g right parenthesis are negative 2021.0 blank k J blank m o l to the power of negative 1 end exponent comma blank minus 1575.0 k J blank m o l to the power of negative 1 end exponent and negative 241.8 blank k J blank m o l to the power of negative 1 end exponent respectively. The respective values of their standard entropies are 194.0, 130.0 and 188.0 blank J blank K to the power of negative 1 end exponent blank m o l to the power of negative 1 end exponent. The values of R equals 8.314 blank J blank K to the power of negative 1 end exponent m o l to the power of negative 1 end exponent equals 0.0831 blank L blank b a r blank m o l to the power of negative 1 end exponent K to the power of negative 1 end exponent
    Answer the following questions on the basis of above information
    Heat change occurring during conversion of 1 kg of C a S O subscript 4 times 2 H subscript 2 O left parenthesis s right parenthesis (molar mass 172 g m o l to the power of negative 1 end exponent) of C a S O subscript 4 times 1 half H subscript 2 O left parenthesis s right parenthesis is equal to

    Concrete is produced from a mixture of cement, water and small stones. Small amount of gypsum, C a S O subscript 4 times 2 H subscript 2 O is added in cement production to improve the subsequent hardening of concrete. The elevated temperature during the production of cement may lead to the formation of unwanted hemihydrate
    C a S O subscript 4 times 1 half H subscript 2 O according to reaction,
    C a S O subscript 4 times 2 H subscript 2 O open parentheses s close parentheses rightwards arrow C a S O subscript 4 times 1 half H subscript 2 O open parentheses s close parentheses plus 3 over 2 H subscript 2 O left parenthesis g right parenthesis
    The increment subscript f end subscript H to the power of ⊖ end exponentofC a S O subscript 4 times 2 H subscript 2 O open parentheses s close parentheses comma blank C a S O subscript 4 times 1 half H subscript 2 O open parentheses s close parentheses comma H subscript 2 O left parenthesis g right parenthesis are negative 2021.0 blank k J blank m o l to the power of negative 1 end exponent comma blank minus 1575.0 k J blank m o l to the power of negative 1 end exponent and negative 241.8 blank k J blank m o l to the power of negative 1 end exponent respectively. The respective values of their standard entropies are 194.0, 130.0 and 188.0 blank J blank K to the power of negative 1 end exponent blank m o l to the power of negative 1 end exponent. The values of R equals 8.314 blank J blank K to the power of negative 1 end exponent m o l to the power of negative 1 end exponent equals 0.0831 blank L blank b a r blank m o l to the power of negative 1 end exponent K to the power of negative 1 end exponent
    Answer the following questions on the basis of above information
    Heat change occurring during conversion of 1 kg of C a S O subscript 4 times 2 H subscript 2 O left parenthesis s right parenthesis (molar mass 172 g m o l to the power of negative 1 end exponent) of C a S O subscript 4 times 1 half H subscript 2 O left parenthesis s right parenthesis is equal to

    chemistry-General
    General
    chemistry-

    For an ideal gas, an illustration of three different paths A comma blank open parentheses B plus C close parentheses and left parenthesis D plus E right parenthesis from an initial state P subscript 1 end subscript comma V subscript 1 end subscript comma T subscript 1 end subscript to a final state P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript is shown in the given figure

    Path A represents a reversible isothermal expansion from P subscript 1 end subscript comma V subscript 1 end subscriptto P subscript 2 end subscript comma V subscript 2 end subscript. Path left parenthesis B plus C right parenthesis represents a reversible adiabatic expansion (B) from P subscript 1 end subscript V subscript 1 end subscript comma blank T subscript 1 end subscript toP subscript 3 end subscript comma V subscript 2 end subscript comma blank T subscript 2 end subscript followed by reversible heating the gas at constant volume (C) from P subscript 3 end subscript comma blank V subscript 2 end subscript comma blank T subscript 2 end subscriptto P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript. Path left parenthesis D plus E right parenthesis represents a reversible expansion at constant pressure P subscript 1 end subscript left parenthesis D right parenthesis from P subscript 1 end subscript comma blank V subscript 1 end subscript comma blank T subscript 1 end subscript to P subscript 1 end subscript comma blank V subscript 2 end subscript comma blank T subscript 3 end subscript followed by a reversible cooling at constant volume V subscript 2 end subscript left parenthesis E right parenthesis from P subscript 1 end subscript comma blank V subscript 2 end subscript comma blank T subscript 3 end subscript to P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript
    What is q subscript r e v end subscript , for path left parenthesis A right parenthesis?

    For an ideal gas, an illustration of three different paths A comma blank open parentheses B plus C close parentheses and left parenthesis D plus E right parenthesis from an initial state P subscript 1 end subscript comma V subscript 1 end subscript comma T subscript 1 end subscript to a final state P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript is shown in the given figure

    Path A represents a reversible isothermal expansion from P subscript 1 end subscript comma V subscript 1 end subscriptto P subscript 2 end subscript comma V subscript 2 end subscript. Path left parenthesis B plus C right parenthesis represents a reversible adiabatic expansion (B) from P subscript 1 end subscript V subscript 1 end subscript comma blank T subscript 1 end subscript toP subscript 3 end subscript comma V subscript 2 end subscript comma blank T subscript 2 end subscript followed by reversible heating the gas at constant volume (C) from P subscript 3 end subscript comma blank V subscript 2 end subscript comma blank T subscript 2 end subscriptto P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript. Path left parenthesis D plus E right parenthesis represents a reversible expansion at constant pressure P subscript 1 end subscript left parenthesis D right parenthesis from P subscript 1 end subscript comma blank V subscript 1 end subscript comma blank T subscript 1 end subscript to P subscript 1 end subscript comma blank V subscript 2 end subscript comma blank T subscript 3 end subscript followed by a reversible cooling at constant volume V subscript 2 end subscript left parenthesis E right parenthesis from P subscript 1 end subscript comma blank V subscript 2 end subscript comma blank T subscript 3 end subscript to P subscript 2 end subscript comma blank V subscript 2 end subscript comma blank T subscript 1 end subscript
    What is q subscript r e v end subscript , for path left parenthesis A right parenthesis?

    chemistry-General
    parallel
    General
    maths-

    If t is parameter, A = (aSec t, bTan t) and B = (-aTan t, bSec t), O = (0, 0) then the locus of the centroid of straight capital delta OAB is

    If t is parameter, A = (aSec t, bTan t) and B = (-aTan t, bSec t), O = (0, 0) then the locus of the centroid of straight capital delta OAB is

    maths-General
    General
    maths-

    A straight line of length 9 units slides with its ends A, B always on x and y axes respectively. Locus of centroid of straight capital delta OAB is

    A straight line of length 9 units slides with its ends A, B always on x and y axes respectively. Locus of centroid of straight capital delta OAB is

    maths-General
    General
    physics-

    If the earth were to suddenly contract so that its radius become half of it present radius, without any change in its mass, the duration of the new day will be....

    If the earth were to suddenly contract so that its radius become half of it present radius, without any change in its mass, the duration of the new day will be....

    physics-General
    parallel
    General
    Maths-

    If the angles of the Δ ABC are in A.P then 3R2=1

    s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

    If the angles of the Δ ABC are in A.P then 3R2=1

    Maths-General

    s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

    General
    physics-

    Two circular loop A & B of radius rA and  rrespectively are made from a uniform wire. The ratio of their moment of inertia about axes passing through their center and perpendicular to their planes is I subscript B over I subscript A equals 8 times text  then  end text fraction numerator r b over denominator r a end fraction  is equal to...

    Two circular loop A & B of radius rA and  rrespectively are made from a uniform wire. The ratio of their moment of inertia about axes passing through their center and perpendicular to their planes is I subscript B over I subscript A equals 8 times text  then  end text fraction numerator r b over denominator r a end fraction  is equal to...

    physics-General
    General
    Maths-

    In straight capital delta A B C comma c left parenthesis a cos space B minus b cos space A right parenthesis equals

    s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

    In straight capital delta A B C comma c left parenthesis a cos space B minus b cos space A right parenthesis equals

    Maths-General

    s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

    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.