We got this question the other day and I'm not exactly sure how to do it.

Given A+B+C= pi

Prove:

cos(2A)+cos(2B)+cos(2C)+1 = -4cos(A)cos(B)cos(C)

The hint was to use product formulas.

Can anybody help me with how I would go about doing this?

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- Nov 21st 2008, 02:55 PMShapeshiftTrig identity
We got this question the other day and I'm not exactly sure how to do it.

Given A+B+C= pi

Prove:

cos(2A)+cos(2B)+cos(2C)+1 = -4cos(A)cos(B)cos(C)

The hint was to use product formulas.

Can anybody help me with how I would go about doing this? - Nov 21st 2008, 04:44 PMTheEmptySetHere is the idea

using your hint the product identity is

using the product identiy again (twice) we end up with

now we use the fact that and

notice that

and finally

sub these into the above and use the sum identity for cosine and you should be done.

(Wink) - Nov 21st 2008, 05:09 PMShyam