Sin^2x-cos^2x
is a trig ratio piece
= 1
sin^2 x + cos^2 x = 1
but
since cos (2x) = cos^2 x - sin^2 x
sin^2 x-cos^2 x = - sin(2x)
argggh
meant to say:
sin^2 x - cos^2 x = - cos(2x)
To simplify the expression sin^2x - cos^2x, we can use the identity for the difference of squares:
a^2 - b^2 = (a + b)(a - b)
In this case, a = sinx and b = cosx.
Let's substitute these values into the formula:
(sin^2x - cos^2x) = (sinx + cosx)(sinx - cosx)
So, the simplified expression is (sinx + cosx)(sinx - cosx).