Question

Prove that (1-2sin²A)/cos⁴A-sin⁴A=2cos²A-1​

Answer 1

Step-by-step explanation:

1-2sin²A = 1 - 2(1 - cos²A)

= 1 - 2 + 2cos²A

= - 1 + 2cos²A

= 2cos²A - 1 --------- (1)

cos⁴A-sin⁴A = (cos²A)² - (sin²A)²

= (cos²A+sin²A) (cos²A-sin²A)

= ( 1 ) (cos²A-sin²A)

= cos²A-sin²A

= cos²A - ( 1 - cos²A )

= cos²A - 1 + cos²A

= 2cos²A - 1 ------------ (2)

from (1) & (2) it is clear that

1-2sin²A = cos⁴A-sin⁴A = 2cos²A-1