Verify the identities.

Question

Cos^2x - sin^2x = 2cos^2x - 1

When verifying identities, can I work on both side?
Ex.
1 - sin^2x - sin^2x = 1 - 2sin^2x
1 - 2sin^2x = 1 - 2sin^2x

Answer 1

cos ^ 2 ( x ) - sin ^ 2 ( x ) = 2 cos ^ 2 ( x ) - 1 Subtract cos ^ 2 ( x ) to both sides

cos ^ 2 ( x ) - sin ^ 2 ( x ) - cos ^ 2 ( x ) = 2 cos ^ 2 ( x ) - 1 - cos ^ 2 ( x )

- sin ^ 2 ( x ) = cos ^ 2 ( x ) - 1 Add 1 to both sides

- sin ^ 2 ( x ) + 1 = cos ^ 2 ( x ) - 1 + 1

1 - sin ^ 2 ( x ) = cos ^ 2 ( x )

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Remark:

1 - sin ^ 2 ( x ) = cos ^ 2 ( x )
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So :

cos ^ 2 ( x ) = cos ^ 2 ( x )