PreCalculus - Trigonometry: Trig Identities (28 of 57) Formula for Lowering Power sin^2(x)=?

In this video I will show how to lower the power or the trigonometric function sin^2(x)=?

[Golden_Tortoise]

At 0:49 I don't understand why the negative was not distributed into the parenthesis to get rid of them like it was done in the previous cos power reduction video:
( 1-sin^2 x ) - sin^2 x thus
-1 +sin^2 x +sin^2 x
in the end I get a slightly different equation: (cos2x + 1)/2 = sin^2 x
Is this wrong?