Question

cos^4A- cos^2A = sin^4A- sin^2A. prove it

Answer 1

(cos² A)² - cos² A
cos² A(cos² A -1)
(1 - sin²A)(-sin² A). [cos²x + sin² x=1]
-sin² A+sin⁴A
sin⁴ A -sin² A.
hence proved.
hope.it helps.
please mark this as brainliest answer.

Answer 2

Taking LHS,

= cos⁴A - cos²A

cos²A as common factor.

= cos²A( cos²A - 1)

= -cos²A(1 - cos²A)

We know that,

• 1 - cos²A = sin²A

= cos²A.sin²A

we know that,

• cos²A = 1 - sin²A

= 1 - sin²A.sin²A

= sin²A - sin⁴A

sin⁴A - sin²A

Hence, Proved !!