Question

sin⁴A-cos⁴A=sin²A-cos²A prove this

Answer 1

LHS = sin^4 A - cos^4 A
= ( sin^2 A - cos^2 A) ( sin^2 A + cos ^2 A)

Since
a^2-b^2 = (a+b)(a-b)

Thus,
= (sin^2 A - cos ^2 A)(sin^2 A + cos^2 A)
= ( sin^2 A - cos^2 A) ( 1)

Because
sin^2 A + cos^2 A = 1

= ( sin^2 A - cos ^2 A)
= RHS.


Hope this helps you !!

Answer 2

Hope this answer is helpful...