# Another Identities Crisis

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• January 14th 2007, 12:22 PM
CaptainBlack
Quote:

Originally Posted by Freaky-Person
They're not. We have some identites but not these ones. All we have is 8 of the easiest ones. Anything multiplied or divided by two, or even associated with the angles is in the AP or Pre-calculus course. This is Canada for you...

Some of these are relatively trivial results of the sum and difference identities:

$\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)$

Put $A=B$:

$\cos(2A)=\cos^2(A)-\sin^2(A)$

then using Pythagoras's theorem in the form:

$\cos^2(x)+\sin^2(x)=1$

we get:

$\cos(2A)=2\cos^2(A)-1$

and

$\cos(2A)=1-2\sin^2(A)$

and by putting $a=2A$

$\cos(a)=2\cos^2(a/2)-1$

and

$\cos(a)=1-2\sin^2(a/2)$

RonL
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