Prove that: from Mathematics Trigonometric Functions
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    Trigonometric Functions

    Multiple Choice QuestionsShort Answer Type

    121.

    Prove the following:

    space space space cot space 4 straight x space left parenthesis sin space 5 straight x space plus space sin space 3 straight x right parenthesis space equals space cot space straight x space left parenthesis sin space 5 straight x space minus space sin space 3 straight x right parenthesis


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    122.

    Prove the following:

    sin space 2 straight x space plus space 2 space sin space 4 straight x space plus space sin space 6 straight x space equals space 4 cos squared space straight x space sin space 4 straight x



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    123.

    Prove that:

    2 space cos straight pi over 13 space cos fraction numerator 9 straight pi over denominator 13 end fraction plus cos fraction numerator 3 straight pi over denominator 13 end fraction plus cos fraction numerator 5 straight pi over denominator 13 end fraction space equals space 0

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    124.

    Prove that:

    cosα space plus space cosβ space plus space cosγ space plus space cos space left parenthesis straight alpha space plus space straight beta space plus space straight gamma right parenthesis space equals space 4 cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight beta plus straight gamma over denominator 2 end fraction close parentheses space cos fraction numerator straight gamma plus straight alpha over denominator 2 end fraction.

    L.H.S. = space space cosα space plus space cosβ space plus space cosγ space plus space cos space left parenthesis straight alpha plus straight beta plus straight gamma right parenthesis

             equals space left square bracket space cosα space plus space cosβ right square bracket space plus space left square bracket cos space left parenthesis straight alpha plus straight beta plus straight gamma right parenthesis space plus space cosγ right square bracket

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              equals space 2 space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses space plus space 2 space cos open parentheses fraction numerator straight alpha plus straight beta plus 2 straight gamma over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses  

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       equals space 2 space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space open square brackets cos open parentheses fraction numerator straight alpha plus straight beta plus 2 straight gamma over denominator 2 end fraction close parentheses plus cos open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses close square brackets

       equals space 2 space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses open square brackets 2 space cos open parentheses fraction numerator begin display style fraction numerator straight alpha plus straight beta plus 2 straight gamma over denominator 2 end fraction end style plus begin display style fraction numerator straight alpha minus straight beta over denominator 2 end fraction end style over denominator 2 end fraction close parentheses close square brackets. space cos open parentheses fraction numerator begin display style fraction numerator straight alpha plus straight beta plus 2 straight gamma over denominator 2 end fraction end style minus begin display style fraction numerator straight alpha minus straight beta over denominator 2 end fraction end style over denominator 2 end fraction close parentheses

       equals space 4 space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator 2 straight alpha plus 2 straight gamma over denominator 4 end fraction close parentheses space cos open parentheses fraction numerator 2 straight beta plus 2 straight gamma over denominator 4 end fraction close parentheses

        equals space 4 space cos open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight beta plus straight gamma over denominator 2 end fraction close parentheses space cos open parentheses fraction numerator straight gamma plus straight alpha over denominator 2 end fraction close parentheses = R.H.S.

    Hence,   L.H.S. = R.H.S.

       

       



            

              

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    125.

    If cos (A + B) sin (C - D) = cos (A - B) sin (C + D)

    Show that:  tan A tan B tan C + tan D = 0

    117 Views
    Answer
    126.

    If sin space straight theta space equals space straight n space sin space left parenthesis straight theta space plus space 2 straight alpha right parenthesis comma show that tan space left parenthesis straight theta space plus space straight alpha right parenthesis space equals space fraction numerator 1 plus straight n over denominator 1 minus straight n end fraction space tanα.

    117 Views
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    127.

    Show that:  left parenthesis sin space 3 straight x space plus space sin space straight x right parenthesis space sin space straight x space plus space left parenthesis cos space 3 straight x space minus space cos space straight x right parenthesis space cosx space equals space 0

    142 Views
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    128. Find the principal solutions (0 ≤ x ≤ 2π ) of the following equation:

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    121 Views
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    129. Find the principal solutions (0 ≤ x ≤ 2π ) of the following equation:

    cos space straight x space equals space minus fraction numerator 1 over denominator square root of 2 end fraction
    125 Views
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    130. Find the principal solutions (0 ≤ x ≤ 2π ) of the following equation:

    space space space tan space straight x space equals space minus square root of 3
    123 Views
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