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Trigonometry – Proving Questions Are Good!

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Tuition given in the topic of A-Maths Tuition Questions from the desk of Miss Loi at 7:11 pm (Singapore time)

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Proving questions are good.
Proving questions are important.
Proving questions helps you remember the formulas.
So don’t be lazy and don’t always skip the proving questions in your homework!

Show that

{2-cosec^2 x}/{cosec^2 x+2 cot x}={sin x-cos x}/{sin x+cos x}

Ignore at your peril!

頑張って!!!

Revision Exercise

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Comments & Reactions

4 Comments

  1. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    26
    Wed
    4:14pm
     
    1

    ok tis q wasted 20mins of my life-.- its simply silly>.

  2. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    26
    Wed
    4:16pm
     
    2

    er..zz got canceled

    let a be cot x
    and cosec^2 x = 1+ cot^2 x

    hence after subing it becomes
    (1-a^2) / (1 +a^2 + 2a)

    =(1-a) (1+a) / (a+1) (a+1)

    = (1-a) / (a+1)
    hence after doin mumbo jumpo = solved

  3. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    28
    Fri
    4:52pm
     
    3

    Kiroii,

    Miss Loi hereby reproduces your workings above for better readability:

    {2-cosec^2x}/{cosec^2 x+2cot x}

    Substituting your trigo identity cosec2x = 1 + cot2x, you'll get:

    {2-(1+cot^2x)}/{(1+cot^2x)+2cot x}
    = {1+cot^2x}/{1+cot^2x+2cot x}

    Factorizing:

    {(1+cot x)(1-cot x)}/{(1+cot x)^2}
    = {(1-cot x)}/{(1+cot x)}

    Now here are the 'mumbo jumpo' parts you're too lazy to write down! (marks may be deducted in exams for insufficient workings - esp for proving questions!)

    Substituting cot x = {cos x}/{sin x}, you'll get:

    {1-{cos x}/{sin x}}/{1+{cos x}/{sin x}}
    = {{sin x - cos x}/{sin x}}/{{sin x + cos x}/{sin x}}
    = {sin x - cos x}/{sin x + cos x}

    So where's the silliness that wasted 20mins of your life??? Tsk.

  4. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    28
    Fri
    11:27pm
     
    4

    de silliness is in my lack of experience..din memorise the whole trigeometry formulas thus wasted quite some time staring thinking of an explicable method..but once i refered to my textbook..w00t brainstorm LOL rather silly?

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