Maths-
General
Easy

Question

In straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals

  1. 0
  2. 1
  3. 1 half
  4. 2R

hintHint:

The law of sines says that the ratio of the sine of one angle to the opposite side is the same ratio for all three angles.law of sinesIn this question, we have to find value of straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis.

The correct answer is: 0


    In straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals
    space In space straight triangle A B C comma
sum a left parenthesis sin space B minus sin space C right parenthesis space equals space a left parenthesis sin space B minus sin space C right parenthesis space plus b left parenthesis sin space C minus sin space A right parenthesis space plus c left parenthesis sin space A minus sin space B right parenthesis space
space a left parenthesis sin space B minus sin space C right parenthesis space plus b left parenthesis sin space C minus sin space A right parenthesis space plus c left parenthesis sin space A minus sin space B right parenthesis space
bold italic T bold italic h bold italic e bold space bold italic a bold italic n bold italic g bold italic l bold italic e bold italic s bold space bold italic o bold italic f bold space bold italic t bold italic h bold italic e bold space bold italic t bold italic r bold italic i bold italic a bold italic n bold italic g bold italic l bold italic e bold space bold italic A bold italic B bold italic C bold space bold italic a bold italic r bold italic e bold space bold italic d bold italic e bold italic n bold italic o bold italic t bold italic e bold italic d bold space bold italic b bold italic y bold space bold italic A bold comma bold space bold italic B bold comma bold space bold italic C bold space bold italic a bold italic n bold italic d bold space bold italic t bold italic h bold italic e bold space bold italic c bold italic o bold italic r bold italic r bold italic e bold italic s bold italic p bold italic o bold italic n bold italic d bold italic i bold italic n bold italic g bold space bold italic o bold italic p bold italic p bold italic o bold italic s bold italic i bold italic t bold italic e bold space bold italic s bold italic i bold italic d bold italic e bold italic s bold space bold italic b bold italic y bold space bold italic a bold comma bold space bold italic b bold comma bold space bold italic c bold.
fraction numerator bold a over denominator bold s bold i bold n bold A end fraction bold space bold space bold equals bold space fraction numerator bold b over denominator bold s bold i bold n bold B end fraction bold space bold equals fraction numerator bold space bold c over denominator bold s bold i bold n bold C end fraction bold space bold equals bold space bold 2 bold italic R bold.
a left parenthesis sin space B minus sin space C right parenthesis space plus b left parenthesis sin space C minus sin space A right parenthesis space plus c left parenthesis sin space A minus sin space B right parenthesis space
a left parenthesis fraction numerator straight b over denominator 2 R end fraction minus fraction numerator space straight c over denominator 2 R end fraction right parenthesis space plus b left parenthesis fraction numerator space straight c over denominator 2 R end fraction minus fraction numerator straight a over denominator 2 straight R end fraction right parenthesis space plus c left parenthesis fraction numerator straight a over denominator 2 R end fraction minus fraction numerator straight b over denominator 2 R end fraction right parenthesis space
fraction numerator ab over denominator 2 R end fraction minus fraction numerator space a straight c over denominator 2 R end fraction plus fraction numerator space b straight c over denominator 2 R end fraction minus fraction numerator ba over denominator 2 straight R end fraction plus fraction numerator ca over denominator 2 R end fraction minus fraction numerator cb over denominator 2 R end fraction space bold rightwards double arrow bold space bold 0 bold space

    img

    The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

    Related Questions to study

    General
    Maths-

    The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is

    The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

    The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is

    Maths-General

    The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

    General
    physics-

    The resistance of a resistance thermometer has values  2.71  and  3.70 ohm at  1C  and  10C  The temperature at which the resistance is  3.26 ohm is

    The resistance of a resistance thermometer has values  2.71  and  3.70 ohm at  1C  and  10C  The temperature at which the resistance is  3.26 ohm is

    physics-General
    General
    chemistry-

    Diborane is a Lewis acid forming addition compound B subscript 2 H subscript 6 times 2 N H subscript 3 with N H subscript 3 end subscript, a Lewis base. This

    Diborane is a Lewis acid forming addition compound B subscript 2 H subscript 6 times 2 N H subscript 3 with N H subscript 3 end subscript, a Lewis base. This

    chemistry-General
    parallel
    General
    Maths-

    If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

    if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c .

    If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

    Maths-General

    if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c .

    General
    physics-

    The pressure on a swimmer 20 m below the surface of coater at sea level is

    The pressure on a swimmer 20 m below the surface of coater at sea level is

    physics-General
    General
    chemistry-

    N a O H can’t be stored in

    N a O H can’t be stored in

    chemistry-General
    parallel
    General
    Maths-

    The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is

    A triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

    The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is

    Maths-General

    A triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

    General
    physics-

    Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?

    Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?

    physics-General
    General
    chemistry-

    11H2 1H and 3 1H will have the same

    11H2 1H and 3 1H will have the same

    chemistry-General
    parallel
    General
    Maths-

    The sides of a triangle are sin space alpha comma cos space alpha and square root of 1 plus sin space alpha cos space alpha end root for some 0 less than alpha less than pi over 2.Then the greatest angle of the triangle is

    The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

    law of cosines

    The sides of a triangle are sin space alpha comma cos space alpha and square root of 1 plus sin space alpha cos space alpha end root for some 0 less than alpha less than pi over 2.Then the greatest angle of the triangle is

    Maths-General

    The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

    law of cosines

    General
    physics-

    A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is

    A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is

    physics-General
    General
    physics-

    A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle alpha to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....

    A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle alpha to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....

    physics-General
    parallel
    General
    Maths-

    If the sides of a triangle are in the ratio x colon y colon square root of x squared plus x y plus y squared end root then greatest angle is

    If the sides of a triangle are in the ratio x colon y colon square root of x squared plus x y plus y squared end root then greatest angle is

    Maths-General
    General
    physics-

    A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.

    A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.

    physics-General
    General
    Maths-

    In straight triangle A B C text , if  end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c then 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c 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 triangle A B C text , if  end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c then 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c 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.