how to simplify sin^2-cos^2

Answer 1

We could also use the fundamental trig ID: sin²x + cos²x = 1 instead of the double angle formula for cosine to get either of the following equivalent expressions:

sin²x - cos²x

= sin²x - (1 - sin²x)

= 2sin²x - 1

OR

sin²x - cos²x

= (1 - cos²x) - cos²x

= 1 - 2cos²x

Answer 2

cos²x - sin²x = cos(2x)

So, sin²x - cos²x = - cos(2x)