Maths-
General
Easy

Question

If fraction numerator cos space x over denominator a end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction then fraction numerator a plus c over denominator b plus d end fraction is equal to

  1. a/d
  2. c/d
  3. b/c
  4. d/a

The correct answer is: b/c


    G I v e n comma
fraction numerator cos space x over denominator a end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction space space space space space.......... open parentheses 1 close parentheses
T o space f i n d comma
fraction numerator a plus c over denominator b plus d end fraction

H e r e comma
fraction numerator cos space x over denominator a end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction
fraction numerator cos space x over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals a over c
U sin g space c o m p o n e n d o comma
fraction numerator cos space x plus cos space left parenthesis x plus 2 theta right parenthesis over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals fraction numerator a plus c over denominator c end fraction
U sin g space f o r m u l a space cos A plus cos B equals 2 cos open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses comma
fraction numerator 2 cos open parentheses fraction numerator x plus x plus 2 theta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator x minus open parentheses x plus 2 theta close parentheses over denominator 2 end fraction close parentheses over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals fraction numerator a plus c over denominator c end fraction
fraction numerator 2 cos open parentheses fraction numerator 2 x plus 2 theta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator negative 2 theta over denominator 2 end fraction close parentheses over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals fraction numerator a plus c over denominator c end fraction space space space space space space space space space space open parentheses because cos open parentheses negative theta close parentheses equals cos theta close parentheses
fraction numerator 2 cos open parentheses x plus theta close parentheses cos open parentheses theta close parentheses over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals fraction numerator a plus c over denominator c end fraction space space space space space space space space space space....... open parentheses 2 close parentheses

F r o m space e q n space open parentheses 1 close parentheses comma
fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction
therefore fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals b over c
S u b s t i t u t i n g space t h e space v a l u e space i n space e q n space open parentheses 2 close parentheses comma
fraction numerator 2 b cos open parentheses theta close parentheses over denominator c end fraction equals fraction numerator a plus c over denominator c end fraction
therefore 2 b cos open parentheses theta close parentheses equals a plus c space space space space space space space....... open parentheses 3 close parentheses

N o w comma
fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction space
fraction numerator cos space left parenthesis x plus theta right parenthesis over denominator cos space left parenthesis x plus 3 theta right parenthesis end fraction equals b over d
U sin g space c o m p o n e n d o comma
fraction numerator cos left parenthesis x plus theta right parenthesis plus cos space left parenthesis x plus 3 theta right parenthesis over denominator cos space left parenthesis x plus 3 theta right parenthesis end fraction equals fraction numerator b plus d over denominator d end fraction
U sin g space f o r m u l a space cos A plus cos B equals 2 cos open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses comma
fraction numerator 2 cos open parentheses fraction numerator x plus theta plus x plus 3 theta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator x plus theta minus open parentheses x plus 3 theta close parentheses over denominator 2 end fraction close parentheses over denominator cos space left parenthesis x plus 3 theta right parenthesis end fraction equals fraction numerator b plus d over denominator d end fraction
fraction numerator 2 cos open parentheses fraction numerator 2 x plus 4 theta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator negative 2 theta over denominator 2 end fraction close parentheses over denominator cos space left parenthesis x plus 2 theta right parenthesis end fraction equals fraction numerator b plus d over denominator d end fraction space space space space space space space space space space open parentheses because cos open parentheses negative theta close parentheses equals cos theta close parentheses
fraction numerator 2 cos open parentheses x plus 2 theta close parentheses cos open parentheses theta close parentheses over denominator cos space left parenthesis x plus 3 theta right parenthesis end fraction equals fraction numerator b plus d over denominator d end fraction space space space space space space space space space....... open parentheses 4 close parentheses

F r o m space e q n space open parentheses 1 close parentheses comma
fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction
therefore fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator cos space left parenthesis x plus 3 theta right parenthesis end fraction equals c over d
S u b s t i t u t i n g space t h e space v a l u e space i n space e q n space open parentheses 4 close parentheses comma
fraction numerator 2 c cos open parentheses theta close parentheses over denominator d end fraction equals fraction numerator b plus d over denominator d end fraction
therefore 2 c cos open parentheses theta close parentheses equals b plus d space space space space space space space....... open parentheses 5 close parentheses

therefore fraction numerator a plus c over denominator b plus d end fraction equals fraction numerator 2 b cos open parentheses theta close parentheses over denominator 2 c cos open parentheses theta close parentheses end fraction equals b over c

    Related Questions to study

    General
    Maths-

    If tan space alpha equals P over q where alpha equals 2 beta comma alpha being an acute angle then 1 half left square bracket p cosec space 2 beta plus q sec space 2 beta right square bracket is equal to

    If tan space alpha equals P over q where alpha equals 2 beta comma alpha being an acute angle then 1 half left square bracket p cosec space 2 beta plus q sec space 2 beta right square bracket is equal to

    Maths-General
    General
    maths-

    Let A,B,C be three angles such that A equals pi over 4 and tan space B tan space C equals p . Then, all possible values of P such that A,B,C are the angles of a triangle is

    Let A,B,C be three angles such that A equals pi over 4 and tan space B tan space C equals p . Then, all possible values of P such that A,B,C are the angles of a triangle is

    maths-General
    General
    chemistry-

    is an example for

    is an example for

    chemistry-General
    parallel
    General
    Maths-

    If y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis where A minus B equals pi over 4 then left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent =

    If y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis where A minus B equals pi over 4 then left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent =

    Maths-General
    General
    chemistry-

    What is the hybridization state of benzyl carbonium ion

    What is the hybridization state of benzyl carbonium ion

    chemistry-General
    General
    maths-

    An integral value of a for which there is a solution of the equationa cos space x plus cot space x 1 equals cosec space x is left parenthesis sin space 2 x not equal to 0 right parenthesis

    An integral value of a for which there is a solution of the equationa cos space x plus cot space x 1 equals cosec space x is left parenthesis sin space 2 x not equal to 0 right parenthesis

    maths-General
    parallel
    General
    Maths-

    If sin space x plus cosec space x plus tan space y plus cot space y equals 4 where x and y element of open parentheses 0 comma pi over 2 close parentheses tan space y over 2 s a root of the equation

    If sin space x plus cosec space x plus tan space y plus cot space y equals 4 where x and y element of open parentheses 0 comma pi over 2 close parentheses tan space y over 2 s a root of the equation

    Maths-General
    General
    biology

    The direction of the water flow in given cells X,Y & Z can be presented as :

    The direction of the water flow in given cells X,Y & Z can be presented as :

    biologyGeneral
    General
    Maths-

    If x over y equals fraction numerator cos begin display style space end style A over denominator cos begin display style space end style B end fraction then fraction numerator x tan space A plus y tan space B over denominator x plus y end fraction=

    If x over y equals fraction numerator cos begin display style space end style A over denominator cos begin display style space end style B end fraction then fraction numerator x tan space A plus y tan space B over denominator x plus y end fraction=

    Maths-General
    parallel
    General
    chemistry-

    The IUPAC name for

    The IUPAC name for

    chemistry-General
    General
    chemistry-

    The IUPAC name of

    The IUPAC name of

    chemistry-General
    General
    chemistry-

    The IUPAC name of the compound shown below is

    The IUPAC name of the compound shown below is

    chemistry-General
    parallel
    General
    chemistry-

    The IUPAC name of the compound

    The IUPAC name of the compound

    chemistry-General
    General
    maths-

    cos space 56 to the power of ring operator plus cos space 58 to the power of ring operator minus cos space 66 to the power of ring operator minus 4 cos space 28 to the power of ring operator cos space 29 to the power of ring operator sin space 33 to the power of ring operator

    cos space 56 to the power of ring operator plus cos space 58 to the power of ring operator minus cos space 66 to the power of ring operator minus 4 cos space 28 to the power of ring operator cos space 29 to the power of ring operator sin space 33 to the power of ring operator

    maths-General
    General
    chemistry-

    Which of the following compounds has wrong IUPAC name?

    Which of the following compounds has wrong IUPAC name?

    chemistry-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.