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Trigonometry – Proving Questions Are Good!

(4)
Posted at 7:11 pm by Miss Loi in A-Maths Questions

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!

がんばって!!!
Miss Loi
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4 Comments

  1. kiroii's Avatar
    kiroii says
    水
    曜
    日
    2007
    Sep
    26
    Wed
    4:14pm
     
    1

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

    Reply kiroii
  2. kiroii's Avatar
    kiroii says
    水
    曜
    日
    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

    Reply kiroii
  3. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi says
    金
    曜
    日
    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.

    Reply Miss Loi
  4. kiroii's Avatar
    kiroii says
    金
    曜
    日
    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?

    Reply kiroii

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