Question

Prove that sin⁴A -cos⁴A=2sin²A-1

Answer 1

sin⁴A-cos⁴A = (sin²A)² - (cos²A)²

= (sin²A+cos²A) (sin²A-cos²A)

= (sin²A+cos²A) (sin²A-cos²A) (a²-b²= (a+b) (a-b))

= 1 (sin²A-cos²A)

= 1 (sin²A-cos²A) (sin²A+cos²A=1)

= 1 (sin²A - ( 1-sin²A))

= 1 (sin²A - ( 1-sin²A)) (cos²A= 1-sin²A)

= sin²A- (1-sin²A)

= sin²A - 1 + sin²A

=sin²A+sin²A - 1

= 2sin²A-1

Hence Proved

Answer 2

Answer:

i believe you could understand it.

it is very simple.