Maths-
General
Easy
Question
In ![straight triangle A B C comma open parentheses fraction numerator b minus c over denominator a end fraction close parentheses sin invisible function application open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses equals](data:image/png;base64,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)
Hint:
In the given question we will first use the sine rule
. Then after putting the value of a, b and c in terms of sin we will simplify using the trigonometric identities.
The correct answer is: ![sin invisible function application open parentheses fraction numerator B minus C over denominator 2 end fraction close parentheses](data:image/png;base64,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)
By the sine rule, we have
![fraction numerator a over denominator sin space A end fraction equals fraction numerator b over denominator sin space B end fraction equals fraction numerator c over denominator sin space C end fraction](data:image/png;base64,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)
let
=k
a = k sin A, b =k sin B and c = k sin C
Now, ![open parentheses fraction numerator b minus c over denominator a end fraction close parentheses space sin space fraction numerator B plus C over denominator 2 end fraction](data:image/png;base64,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)
![equals open parentheses fraction numerator k space sin space B space minus space k space sin space C space over denominator k sin space A end fraction close parentheses sin open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses
equals open parentheses fraction numerator space sin space B space minus space space sin space C space over denominator sin space A end fraction close parentheses sin open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses
equals fraction numerator 2 cos open parentheses begin display style fraction numerator B plus C over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator B minus C over denominator 2 end fraction end style close parentheses over denominator 2 sin begin display style A over 2 end style cos begin display style A over 2 end style end fraction sin open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space open square brackets sin space A minus space sin space B equals 2 space cos space open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses close square brackets
equals fraction numerator cos open parentheses begin display style straight pi over 2 end style minus begin display style A over 2 end style close parentheses sin space open parentheses fraction numerator B minus C over denominator 2 end fraction close parentheses sin space open parentheses begin display style straight pi over 2 end style minus begin display style A over 2 end style close parentheses over denominator sin A over 2 cos A over 2 end fraction space space space space space space space space space space space space space space space space space space space space space open square brackets A plus B plus C equals straight pi comma space fraction numerator straight A plus straight B plus straight C over denominator 2 end fraction equals straight pi over 2 comma space fraction numerator straight B plus straight C over denominator 2 end fraction equals straight pi over 2 minus straight A over 2 close square brackets
equals fraction numerator sin begin display style A over 2 end style sin begin display style fraction numerator B minus C over denominator 2 end fraction end style cos begin display style A over 2 end style over denominator sin begin display style A over 2 end style cos begin display style A over 2 end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets cos open parentheses straight pi over 2 minus A over 2 close parentheses equals sin A over 2 comma sin space open parentheses straight pi over 2 minus A over 2 close parentheses equals cos A over 2 close square brackets
equals sin open parentheses fraction numerator B minus C over denominator 2 end fraction close 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)
Related Questions to study
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An antenna behaves as resonant circuit only when its length is
An antenna behaves as resonant circuit only when its length is
physics-General
Maths-
If ![A equals 60 to the power of ring operator text then the value of end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals](data:image/png;base64,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)
If ![A equals 60 to the power of ring operator text then the value of end text open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses equals](data:image/png;base64,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)
Maths-General
physics-
In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (
) will be equal to
![](data:image/png;base64,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)
In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air (
) will be equal to
![](data:image/png;base64,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)
physics-General
chemistry-
Which statement is not correct for n=5,m=2:
Which statement is not correct for n=5,m=2:
chemistry-General
chemistry-
In P-atom find out the no. of paired electrons for l=1 and m =0-
In P-atom find out the no. of paired electrons for l=1 and m =0-
chemistry-General
chemistry-
For H- atom, the energy required for the removal electron from various sub-shells is given at under:
The order of the energies would be:
For H- atom, the energy required for the removal electron from various sub-shells is given at under:
The order of the energies would be:
chemistry-General
physics-
Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in
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)
Immiscible transparent liquids A, B, C, D and E are placed in a rectangular container of glass with the liquids making layers according to their densities. The refractive index of the liquids are shown in the adjoining diagram. The container is illuminated from the side and a small piece of glass having refractive index 1.61 is gently dropped into the liquid layer. The glass piece as it descends downwards will not be visible in
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)
physics-General
Maths-
Values of
is :
Values of
is :
Maths-General
physics-
A rectangular tank of depth 8 meter is full of water (
), the bottom is seen at the depth
A rectangular tank of depth 8 meter is full of water (
), the bottom is seen at the depth
physics-General
chemistry-
A photon of energe12.75ev is completely absorbed by a hydrogen atom initially in ground sate. The principle quantum number of the excited state is:
A photon of energe12.75ev is completely absorbed by a hydrogen atom initially in ground sate. The principle quantum number of the excited state is:
chemistry-General
chemistry-
A certain electronic transition from an excited statetothegroundstateoftheH2 atom in one or more steps gives rise to four lines in the ultra violet region of the spectrum, how many lines does this transition produce in the infrared region of the spectrum-
A certain electronic transition from an excited statetothegroundstateoftheH2 atom in one or more steps gives rise to four lines in the ultra violet region of the spectrum, how many lines does this transition produce in the infrared region of the spectrum-
chemistry-General
chemistry-
Find out ratio of following for photon (νmax.) Lyman: (νmax) Brackett-
Find out ratio of following for photon (νmax.) Lyman: (νmax) Brackett-
chemistry-General
chemistry-
The potential energies of first, second and third Bohr’s orbits of He+ cation are E1,E2 and E3. The correct sequence of these energies is-
The potential energies of first, second and third Bohr’s orbits of He+ cation are E1,E2 and E3. The correct sequence of these energies is-
chemistry-General
Maths-
In ![straight triangle A B C comma left parenthesis a minus b right parenthesis squared cos squared invisible function application c over 2 plus left parenthesis a plus b right parenthesis squared sin squared invisible function application c over 2 equals](data:image/png;base64,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)
In ![straight triangle A B C comma left parenthesis a minus b right parenthesis squared cos squared invisible function application c over 2 plus left parenthesis a plus b right parenthesis squared sin squared invisible function application c over 2 equals](data:image/png;base64,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)
Maths-General
maths-
Tangents drawn to parabola
= 4ax at the points A and B intersect at C. Ordinate of A, C and B forms
Tangents drawn to parabola
= 4ax at the points A and B intersect at C. Ordinate of A, C and B forms
maths-General