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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: BlueYoHo on March 09, 2009, 02:15:06 pm

Title: Trig proof...
Post by: BlueYoHo on March 09, 2009, 02:15:06 pm: I don't understand how $sin^4x - cos^4x = -cos2x$
I know $cos2x = cos^2x - sin^2x$
And I'm assuming that because it's $sinx - cosx$ instead of $cosx - sinx$ that it is negative $cos2x$
But since it's $sin^4x$ and $cos^4x$ shouldn't it equal something like $-cos4x$ ?

Can someone please go through the steps...Thanks in advance :)
Title: Re: Trig proof...
Post by: kurrymuncher on March 09, 2009, 02:21:38 pm: hint: use the difference of two squares rule.

You should end up with: (sinx^2 +cosx^2)( sinx^2-cosx^2)

Because (sinx^2 +cosx^2)=1, that means the answer is actually ( sinx^2-cosx^2), which is Cos2x multiplied by -1

sorry cbf using latex
Title: Re: Trig proof...
Post by: BlueYoHo on March 09, 2009, 02:29:36 pm: OOOOOOOOOOOOOOOOOOOOHHHHHHHHHHHHHHHHHHHHHH now I get it.

Lol, thanks heaps man.