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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: fredrick on November 01, 2008, 09:35:37 pm

Title: Trig proofs
Post by: fredrick on November 01, 2008, 09:35:37 pm: To proof one side is equal to the other do you simplify one side to make it look like the other or can you simplify both sides simultaneously until both sides are the same?
Title: Re: Trig proofs
Post by: /0 on November 01, 2008, 09:40:06 pm: You need to simplify one side to make it look like the other. Otherwise you are assuming that they are the same to begin with, which is a fallacy.

However, you can also do this:

To Prove: $(\tan{x}\cos{x})^2 = 1-\frac{1}{2}(\cos{(2x)}+1)$

$LHS = \left(\sin{x}\right)^2$
$=\sin^2{x}$

$RHS = 1-\frac{1}{2}(2\cos^2{x})$
$=1-\cos^2{x}$
$=\sin^2{x}$

LHS = RHS, as required.
Title: Re: Trig proofs
Post by: fredrick on November 01, 2008, 09:43:54 pm: oh right! thanks