O Level Additional Math – How To Prove Trigonometry Identity

Written on September 29, 2008 by Ai Ling in A-Maths, Weekly Question
5 Comments
Dear Ms Ong,
i had just taken my class test on simple trigonometric identities and well as further trignonometric identities yesterday.
sadly to say, i left all the proving of trigonometric identities blank which is worth a total of 9 marks.
Im starting to get panic about trigonometric identities for my coming common test,end of year exams as well as the big O Level.
so im actually here to ask you if you may guide me on how to do them in a faster way, because i realised ive no time to tackle those proving questions.
Best Wishes,
Priscilla Fong

I received this email among the many others in my mailbox. I think this is a common problem face in proving Trigo Identity question. I shall provide a few strategies to handle this sort of question.

  • Usually start with the left hand side or whichever side which is more complicated.
  • When given trigo functions in the form of sec, cosec or cot x , it is advisable to change it to basic trigo functions like sin, cos, tan
  • When question involves power (especially square power), formulas should be considered.
  • Have the END in mind before you begin i.e if the end result involves only sin, your working should eventually eliminate the other trigo functions and stick on to sin.
  • It should take less than 8 steps for a 3-4 marks proving question.
  • a^2-b^2=(a+b)(a-b) is sometimes used in proving Trigo Identity. (Algebra rule)

I am going to use an example to illustrate how to use the above strategies

Q: Prove the identity (sec A - tan A)^2 = {1- sin A}/{1+ sin A}

(sec A - tan A)^2 =( {1}/{ cos A}-{sin A}/{cos A})^2 (Change sec and tan into sin & cos)

=  ( {1 - sin A}/{cos A})^2

= {(1-sin A)^2}/{(cos A)^2} 

=  {(1 - sin A)(1 - sin A)}/{(1 - sin^2 A)} (applying formula)

= {(1 - sin A)(1 - sin A)}/{(1 - sin A)(1 + sin A)}  (applying algebraic rule)

= {1 - sin A}/{1 + sin A}  (Proven)

Total number of steps = 6

Additional resource: You may want to read on A-Math Trigo Graphs here.

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5 Comments - Leave your comment!
5 Responses to O Level Additional Math – How To Prove Trigonometry Identity
  1. O Level A-Math Trigonometry Basics : How Do We Know Which Formula To Use?
    July 4, 2009 | 6:29 pm

    [...] How To Prove Trigonometry Identity [...]

  2. manasseh
    July 25, 2010 | 5:20 am

    how do i master proving of trig identities with ease…i will be glad if i can get a summary note on the proving and tips in proving from u

    Reply

  3. Anthony
    April 24, 2011 | 1:18 pm

    This example is wrong and makes no sense. (1-sin)^2 equals (1-sin)(1+sin)

    Reply

    Ai Ling Reply:
    April 27th, 2011 at 10:24 am

    Anthony:
    (1-sinx)^2 = (1-sinx)(1-sinx)
    1-sin^2x = (1-sinx)(1+sinx)
    Note: sin^2x is read as sin square x

    (a-b)^2=(a-b)(a-b)
    (a^2-b^2)=(a-b)(a+b)

    Everything is correct in the example.

    Reply

  4. simon ng'uni
    September 16, 2011 | 7:37 am

    i dont still understand

    Reply

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