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# C3 Identify proof question Watch

1. I have no idea how I have messed up this identity proof question

Prove: Cos4x is identical to 8cos^(4)x-8cos^(2)x+1

I started with the left hand side, rewriting it as

Cos(2x+2x)

I then used the compound formula to obtain

cos2xcos2x-sin2xsin2x

Using double angle formulae

(cos^(2)x-sin^(2)x)^(2) - (2sinxcosx)^2

Expanding the squared brackets to obtain

cos^(4)x-2cos^(2)xsin^(2)x+sin^(4)x+4sin^ (2)xcos^(2)x

Collecting like terms

sin^(4)x+cos^(4)x+2cos^(2)xsin^( 2)x

Using the identity sin^(2)x = 1-cos^(2)x and expanding the bracket

sin^(4)x+cos^(4)x+2cos^(2)x-2cos^(4)x

Collecting like terms again

sin^(4)x-cos^(4)x+2cos^(2)x

Using the identity sin^(4)x = (1-cos^(2)x)^(2)

1-2cos^(2)x+cos^(4)x-cos^(4)x-2cos^(2)x

Collecting like terms for the last time cancels out the trig terms, leaving just...

1

I know this is a lot of workings, but can somebody please tell me where I've gone wrong?
2. (Original post by jamb97)
I have no idea how I have messed up this identity proof question

Prove: Cos4x is identical to 8cos^(4)x-8cos^(2)x+1

I started with the left hand side, rewriting it as

Cos(2x+2x)

I then used the compound formula to obtain

cos2xcos2x-sin2xsin2x

Using double angle formulae

(cos^(2)x-sin^(2)x)^(2) - (2sinxcosx)^2

Expanding the squared brackets to obtain

cos^(4)x-2cos^(2)xsin^(2)x+sin^(4)x+4sin^(2)xcos^(2)x
First error - in red - should be minus.

Not checked the rest.
3. (Original post by ghostwalker)
First error - in red - should be minus.

Not checked the rest.
But why? Surely if you square that you will get a positive...?

EDIT: Nevermind, I see what has gone wrong. I misinterpreted my own working... Thank you very much! :P

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