Precalculus
posted by Shadow on .
Verify the identities.
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

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 )
________________________________________
Remark:
1  sin ^ 2 ( x ) = cos ^ 2 ( x )
________________________________________
So :
cos ^ 2 ( x ) = cos ^ 2 ( x )