Question

prove that :



sin^4 - cos^4 = 1 - 2cos^2

Answer 1

Answer:

sin^4 - cos^4 =  (sin^2 + cos^2) * (sin^2 - cos^2)

sin^4 - cos^4 = sin^2 - cos^2      since sin^2 + cos^2 = 1   (I)

sin^2 - cos^2 = 1 - cos^2 - cos^2 = 1 - 2 cos^2  again using (I)