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In order to prove this identity, you need to start with one side, and then using existing identities, end up at the other side of the identity.
`LS=cos^2x-sin^2x` use `sin^2x+cos^2x=1`
`=cos^2x-(1-cos^2x)` remove brackets
`=cos^2x-1+cos^2x` collect like terms
The identity has been proven.
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