Comments on: Trigonometry – Proving Questions Are Good! http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: kiroii http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1191 kiroii Fri, 28 Sep 2007 15:27:27 +0000 http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1191 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? 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?

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1183 Miss Loi Fri, 28 Sep 2007 08:52:24 +0000 http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1183 Kiroii, Miss Loi hereby reproduces your workings above for better readability: <m>{2-cosec^2x}/{cosec^2 x+2cot x}</m> Substituting your trigo identity cosec<sup>2</sup><var>x</var> = 1 + cot<sup>2</sup><var>x</var>, you'll get: <m>{2-(1+cot^2x)}/{(1+cot^2x)+2cot x}</m> = <m>{1+cot^2x}/{1+cot^2x+2cot x}</m> Factorizing: <m>{(1+cot x)(1-cot x)}/{(1+cot x)^2}</m> = <m>{(1-cot x)}/{(1+cot x)}</m> <span class="highlight">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!)</span> Substituting cot <var>x</var> = <m>{cos x}/{sin x}</m>, you'll get: <m>{1-{cos x}/{sin x}}/{1+{cos x}/{sin x}}</m> = <m>{{sin x - cos x}/{sin x}}/{{sin x + cos x}/{sin x}}</m> = <m>{sin x - cos x}/{sin x + cos x}</m> So where's the silliness that wasted 20mins of your life??? Tsk. 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.

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1159 kiroii Wed, 26 Sep 2007 08:16:46 +0000 http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1159 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 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

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1158 kiroii Wed, 26 Sep 2007 08:14:37 +0000 http://www.exampaper.com.sg/questions/a-maths/trigonometry-proving-questions-are-good#comment-1158 ok tis q wasted 20mins of my life-.- its simply silly>. ok tis q wasted 20mins of my life-.- its simply silly>.

]]>