Question

Prove the following identities:

sin⁴A – cos⁴A = 2sin²A – 1

Answer 1

L.H.S. = sin⁴A – cos⁴A

= (sin²A)² – (cos²A)²

= (sin²A + cos²A)(sin²A – cos²A)

= sin²A – cos²A

= sin²A – (1 – sin²A)

= 2sin²A – 1

= R.H.S.