Maths-
General
Easy

Question

In any straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction =

  1. cos squared space A
  2. cos squared space B
  3. sin squared space A
  4. sin squared space B

hintHint:

In this question, we have to find fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction. For this we will use some trigonometric formula s equals fraction numerator a plus b plus c over denominator 2 end fraction comma space sin space A over 2 equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root space comma space cos space A over 2 equals square root of fraction numerator s left parenthesis s minus a right parenthesis over denominator b c end fraction end root space a n d space sin space 2 A space equals 2. sin space A. cos space A to find the required value.

The correct answer is: sin squared space A


    fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction space space space space space space space space space space
equals fraction numerator 2 s space left parenthesis 2 s minus a minus a right parenthesis left parenthesis 2 s minus b minus b right parenthesis left parenthesis 2 s minus c minus c right parenthesis over denominator 4 b squared c squared end fraction space space space space space space space space space space space space space space space open square brackets s equals fraction numerator a plus b plus c over denominator 2 end fraction close square brackets
equals fraction numerator 2 s.2 left parenthesis s minus a right parenthesis.2 left parenthesis s minus b right parenthesis.2 left parenthesis s minus c right parenthesis over denominator 4 b squared c squared end fraction
equals fraction numerator 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b squared c squared end fraction
equals 4 sin squared A over 2 cos squared A over 2 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 space space space space space space space open square brackets sin space A over 2 equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root comma space cos A over 2 equals square root of fraction numerator s left parenthesis s minus a right parenthesis over denominator b c end fraction end root close square brackets
equals sin squared A 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 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 sin space 2 A equals 2. sin space A. cos space B close square brackets

    Related Questions to study

    General
    Maths-

    In straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis =

    In straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis =

    Maths-General
    General
    Maths-

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

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

    Maths-General
    General
    Maths-

    If the period of fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N is 6 pi then n=

    If the period of fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N is 6 pi then n=

    Maths-General
    parallel
    General
    Maths-

    Let f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where  is the integral part of x. If the period of f(x) is pi, then a element of

    Let f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where  is the integral part of x. If the period of f(x) is pi, then a element of

    Maths-General
    General
    physics-

    Which of the following options is correct for the object having a straight line motion represented by the following graph

    Which of the following options is correct for the object having a straight line motion represented by the following graph

    physics-General
    General
    physics-

    A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

    A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

    physics-General
    parallel
    General
    physics-

    A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from P to Q is 8 m s to the power of negative 1 end exponent and that from Q to Sis 12 m s to the power of negative 1 end exponent. If Q S minus P Q, then the average velocity from P to S is

    A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from P to Q is 8 m s to the power of negative 1 end exponent and that from Q to Sis 12 m s to the power of negative 1 end exponent. If Q S minus P Q, then the average velocity from P to S is

    physics-General
    General
    chemistry-

    i) 

    ii) 

    iii) 

    iv)  Me minus identical to negative straight H rightwards arrow with text  dil.H  end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top

    Which of the statements are correct?

    i) 

    ii) 

    iii) 

    iv)  Me minus identical to negative straight H rightwards arrow with text  dil.H  end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top

    Which of the statements are correct?

    chemistry-General
    General
    physics-

    A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time (t)

    A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time (t)

    physics-General
    parallel
    General
    Maths-

    The value of integer n for which the function f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction has 4 pi as its period is

    The value of integer n for which the function f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction has 4 pi as its period is

    Maths-General
    General
    Maths-

    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

    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

    Maths-General
    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
    parallel
    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
    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
    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.