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.
- [pmath]a^2-b^2=(a+b)(a-b)[/pmath] 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 [pmath](sec A - tan A)^2 = {1- sin A}/{1+ sin A}[/pmath]
[pmath](sec A - tan A)^2 =( {1}/{ cos A}-{sin A}/{cos A})^2[/pmath] (Change sec and tan into sin & cos)
= [pmath]( {1 - sin A}/{cos A})^2[/pmath]
= [pmath]{(1-sin A)^2}/{(cos A)^2} [/pmath]
= [pmath] {(1 - sin A)(1 - sin A)}/{(1 - sin^2 A)} [/pmath] (applying formula)
= [pmath] {(1 - sin A)(1 - sin A)}/{(1 - sin A)(1 + sin A)} [/pmath] (applying algebraic rule)
= [pmath]{1 - sin A}/{1 + sin A} [/pmath] (Proven)
Total number of steps = 6
Additional resource: You may want to read on A-Math Trigo Graphs here.
