How would I 'verify' this problem in pre-calc/trigonometry

(sin^2a) - (sin^4a) = (cos^2a) - (cos^4a)

This (I think) would be spoken as "sine squared of a minus sine to the fourth of a equals cosine squared of a minus cosine to the fourth of a".

Please show steps so that I can learn and find out how to do other problems!

Thanks in advance,
Joey

(sin^2a) - (sin^4a)
= (1-cos²a) - (1 - cos²a)²
= 1-cos²a - (1 - 2cos²a + cos^4a)
= 1-1 - cos²a + 2cos²a - cos^4a
= cos^2a - cos^4a
QED